Particle - St. Louis Public Schools · Web viewThe net electric force acting on a charged particle...
Transcript of Particle - St. Louis Public Schools · Web viewThe net electric force acting on a charged particle...
IB 12
1
Particle Mass Electric Charge
Electron me = 9110 x 10-31 kg q = -eq = -160 x 10-19 C
Proton mp = 1673 x 10-27 kg q = +eq = +160 x 10-19 C
Neutron mn = 1675 x 10-27 kg q = 0q = 0 C
Electrostatics1) electric charge 2 types of electric charge positive and negative
2) charging by friction transfer of electrons from one object to another
3) positive object lack of electrons negative object excess of electrons
Conservation of Electric Charge The total electric charge of an isolated system remains constant
4) Types of materials
a) Conductors materials in which electric charges move freely (eg metals graphite)
b) Insulators materials in which electric charges do not move freely (eg plastic rubber dry wood glass ceramic)
c) Semiconductors materials with electrical properties between those of conductors and insulators (eg silicon)
d) Superconductors materials in which electrical charges move without resistance (eg some ceramics at very low temperatures)
Properties of Atomic Particles
e = elementary unit of charge (magnitude of charge on electron)
e = 160 x 10-19 C
DO 1 A balloon has gained 2500 electrons after being rubbed with wool What is the charge on the balloon What is the charge on the wool
DO 2 A rubber rod acquires a charge of -45 μC How many excess electrons does this represent
IB 12
2
Electric Force (Electrostatic Force Coulomb Force)
Coulombrsquos Law The electric force between two point charges is directly proportional to the product of the two charges and inversely proportional to square of the distance between them and directed along the line joining the two charges
NOTE +-F denotes direction of force not sign of charge
k = Coulomb constant (electrostatic constant)
k = 899 x 109 Nm2 C -2
k = 1 4πε0
ε0 = permittivity of free space = 885 x 10-12 C2 N-1 m -2
Coulomb Force
Point charge a charged object that acts as if all its charge is concentrated at a single point
Alternate formula for Coulomb force
DO Use the Coulomb force to estimate the speed of the electron in a hydrogen atom
IB 12
3
The Principle of Superposition
The net electric force acting on a charged particle is the vector sum of all the electric forces acting on it
DO 1 Determine the net electrostatic force on charge q1 as shown below
DO 2 Where can a third charge of +10 microC be placed so that the net force acting on it is zero
DO 3 Three point charges of -20 microC are arranged as shown Determine the magnitude and direction of the net force on charge q1
IB 12
4
Electric Field
Electric field a region in space surrounding a charged object in which a second charged object experiences an electric force
Test charge a small positive charge used to test an electric field
Electric Field Diagrams (DO ALL 7)1 Positively charged sphere 2 Positive point charge 3 Negative point charge
Radial Field field lines are extensions of radii
4 Two positive charges 5 Two negative charges 6 Two unlike charges
Properties of Electric Field Lines
1 Never cross
2 Show the direction of force on a small positive test charge
3 Out of positive into negative
4 Direction of electric field is tangent to the field lines
5 Density of field lines is proportional to field strength (density = intensity)
6 Perpendicular to surface
7 Most intense near sharp points
7 Oppositely charged parallel plates
Edge Effect bowing of field lines at edges
Uniform Field field has same intensity at all spots
IB 12
5
Electric Field Strength (Intensity) electric force exerted per unit charge on a small positive test charge
Electric Field Strength
Units NC
Electric Field Electric Field for a Point Charge
Point Charge Spherical Conductor
DO 1 a) Find the magnitude and direction of the electric field at a spot 0028 meter away from a sphere whose charge is +354 microcoulombs and whose radius is 060 centimeters
b) Find the magnitude and direction of the electric force acting on a -702 nC charge placed at this spot
c) Find the electric field strength at the surface of the sphere
DO 2 a) Find the magnitude and direction of the gravitational field at an altitude of 100 km above the surface of the Earth
b) Find the magnitude and direction of the gravitational force exerted on a 60 kg bowling ball placed at this spot
c) Find the gravitational field strength at the surface of the Earth
Electric Force
Units N
IB 12
6
DO 3 a) Find the magnitude and direction of the net electric field halfway between the two charges shown below
b) Determine the electric force on a proton placed at this spot
DO 4 Two charged objects A and B each contribute as follows to the net electric field at point P EA = 300 NC directed to the right
and EB = 200 NC directed downward What is the net electric field at P
DO 5 a) Two positive point charges q1 = +16 C and q2 = +40 C are separated in a vacuum by a distance of 30 m Find the
spot on the line between the charges where the net electric field is zero
IB 12
7
DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC
a) Describe the motion of the proton
b) Write an expression for the acceleration of the proton
c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate
DO 7 A particle is shot with an initial speed through the two parallel plates as shown
a) Sketch and describe the path it will take if it is a proton an electron or a neutron
b) Which particle will experience a greater force
c) Which particle will experience a greater acceleration
d) Which particle will experience a greater displacement
DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude
IB 12
8
Electric Potential Energy
Gravitational Potential Energy (EP)
Base level where EP = 0
High amount of EP
Low amount of EP
Reason for EP
1 Test object has mass (test mass = m)
2 Test mass is in a gravitational field (g) caused by larger object (M)
3 Larger object exerts a gravitational force on test mass (Fg = mg)
4 Test mass has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Gravitational potential energyEP = mgh W = ΔEP = mg Δh
Electric Potential Energy (EP)
High amount of EP
Low amount of EP
Reason for EP
1 Test object has charge (test charge = +q)
2 Test charge is in an electric field caused by larger object (Q)
3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Electric potential energyEP = Eq hW = ΔEP = Eq Δh
Base level where EP = 0
Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field
EP = 0(Work done by field)
Derivation for Point Charges
Electric Potential Energy due to a point charge
Formula Units
J
Type
scalar
IB 12
9
Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field
Electric Potential due to a point charge
Formula
Units
JC= volts(V)
Type
scalar
ABHigher potential Lower potential
Zero potential
AB
Lower potential Higher potentialZero potential
DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge
b) How much potential energy will an electron have if it is at this spot
c What is the potential where a proton is placed 096 m from a -12 nC charge
IB 12
10
Point Charges
+Q +Q +Q +Q
Electric Force Electric Field Electric Potential Energy Electric Potential
Two objects needed ndash interaction between the two
Magnitude F = Eq
F = kQqr2
Units N
Type vector
Direction likes repel unlikes attract
Sign donrsquot use when calculating ndash check frame of reference
One object needed ndash property of the field
Magnitude V = EPq
V = kQr
Units JC
Type scalar (+-)
Sign use sign of Q
Two objects needed ndash quantity possessed by the system
Magnitude EP = qV
EP = kQqr
Units J
Type scalar (+-)
Sign use signs of Q and q
One object needed ndash property of that one object
Magnitude E = Fq
E = kQr2
Units NC
Type vector
Direction away from positive towards negative
Sign donrsquot use when calculating ndash check frame of reference
F = 0 where E = 0 EP = 0 where V = 0
IB 12
11
DO 1 a) Calculate the net electric field at each spot (A and B)
b) Calculate the net electric force on a proton placed at each spot
DO 2 a) Calculate the net electric potential at each spot (A and B)
b) Calculate the electric potential energy of a proton placed at each spot
IB 12
12
Electric Potential and Conductors
For a hollow or solid conductor
1 all the charge resides on the outside surface
2 the electric field is zero everywhere within
3 the external electric field acts as if all the charge is concentrated at the center
4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance
Elec
tric
Fiel
d St
reng
th
Value at surface = kQr2
radius
Graphs for a spherical conductor
Distance
Elec
tric
Pote
ntia
l
radius
DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC
a) What is the electric field at the center of the sphere
b) What is the electric field at the surface of the sphere
c) What is the electric field at a distance of 075 m from the surface of the sphere
d) What is the electric potential at the surface of the sphere
e) What is the electric potential at the center of the sphere
f) What is the electric potential at a distance of 075 m from the surface of the sphere
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
2
Electric Force (Electrostatic Force Coulomb Force)
Coulombrsquos Law The electric force between two point charges is directly proportional to the product of the two charges and inversely proportional to square of the distance between them and directed along the line joining the two charges
NOTE +-F denotes direction of force not sign of charge
k = Coulomb constant (electrostatic constant)
k = 899 x 109 Nm2 C -2
k = 1 4πε0
ε0 = permittivity of free space = 885 x 10-12 C2 N-1 m -2
Coulomb Force
Point charge a charged object that acts as if all its charge is concentrated at a single point
Alternate formula for Coulomb force
DO Use the Coulomb force to estimate the speed of the electron in a hydrogen atom
IB 12
3
The Principle of Superposition
The net electric force acting on a charged particle is the vector sum of all the electric forces acting on it
DO 1 Determine the net electrostatic force on charge q1 as shown below
DO 2 Where can a third charge of +10 microC be placed so that the net force acting on it is zero
DO 3 Three point charges of -20 microC are arranged as shown Determine the magnitude and direction of the net force on charge q1
IB 12
4
Electric Field
Electric field a region in space surrounding a charged object in which a second charged object experiences an electric force
Test charge a small positive charge used to test an electric field
Electric Field Diagrams (DO ALL 7)1 Positively charged sphere 2 Positive point charge 3 Negative point charge
Radial Field field lines are extensions of radii
4 Two positive charges 5 Two negative charges 6 Two unlike charges
Properties of Electric Field Lines
1 Never cross
2 Show the direction of force on a small positive test charge
3 Out of positive into negative
4 Direction of electric field is tangent to the field lines
5 Density of field lines is proportional to field strength (density = intensity)
6 Perpendicular to surface
7 Most intense near sharp points
7 Oppositely charged parallel plates
Edge Effect bowing of field lines at edges
Uniform Field field has same intensity at all spots
IB 12
5
Electric Field Strength (Intensity) electric force exerted per unit charge on a small positive test charge
Electric Field Strength
Units NC
Electric Field Electric Field for a Point Charge
Point Charge Spherical Conductor
DO 1 a) Find the magnitude and direction of the electric field at a spot 0028 meter away from a sphere whose charge is +354 microcoulombs and whose radius is 060 centimeters
b) Find the magnitude and direction of the electric force acting on a -702 nC charge placed at this spot
c) Find the electric field strength at the surface of the sphere
DO 2 a) Find the magnitude and direction of the gravitational field at an altitude of 100 km above the surface of the Earth
b) Find the magnitude and direction of the gravitational force exerted on a 60 kg bowling ball placed at this spot
c) Find the gravitational field strength at the surface of the Earth
Electric Force
Units N
IB 12
6
DO 3 a) Find the magnitude and direction of the net electric field halfway between the two charges shown below
b) Determine the electric force on a proton placed at this spot
DO 4 Two charged objects A and B each contribute as follows to the net electric field at point P EA = 300 NC directed to the right
and EB = 200 NC directed downward What is the net electric field at P
DO 5 a) Two positive point charges q1 = +16 C and q2 = +40 C are separated in a vacuum by a distance of 30 m Find the
spot on the line between the charges where the net electric field is zero
IB 12
7
DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC
a) Describe the motion of the proton
b) Write an expression for the acceleration of the proton
c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate
DO 7 A particle is shot with an initial speed through the two parallel plates as shown
a) Sketch and describe the path it will take if it is a proton an electron or a neutron
b) Which particle will experience a greater force
c) Which particle will experience a greater acceleration
d) Which particle will experience a greater displacement
DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude
IB 12
8
Electric Potential Energy
Gravitational Potential Energy (EP)
Base level where EP = 0
High amount of EP
Low amount of EP
Reason for EP
1 Test object has mass (test mass = m)
2 Test mass is in a gravitational field (g) caused by larger object (M)
3 Larger object exerts a gravitational force on test mass (Fg = mg)
4 Test mass has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Gravitational potential energyEP = mgh W = ΔEP = mg Δh
Electric Potential Energy (EP)
High amount of EP
Low amount of EP
Reason for EP
1 Test object has charge (test charge = +q)
2 Test charge is in an electric field caused by larger object (Q)
3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Electric potential energyEP = Eq hW = ΔEP = Eq Δh
Base level where EP = 0
Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field
EP = 0(Work done by field)
Derivation for Point Charges
Electric Potential Energy due to a point charge
Formula Units
J
Type
scalar
IB 12
9
Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field
Electric Potential due to a point charge
Formula
Units
JC= volts(V)
Type
scalar
ABHigher potential Lower potential
Zero potential
AB
Lower potential Higher potentialZero potential
DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge
b) How much potential energy will an electron have if it is at this spot
c What is the potential where a proton is placed 096 m from a -12 nC charge
IB 12
10
Point Charges
+Q +Q +Q +Q
Electric Force Electric Field Electric Potential Energy Electric Potential
Two objects needed ndash interaction between the two
Magnitude F = Eq
F = kQqr2
Units N
Type vector
Direction likes repel unlikes attract
Sign donrsquot use when calculating ndash check frame of reference
One object needed ndash property of the field
Magnitude V = EPq
V = kQr
Units JC
Type scalar (+-)
Sign use sign of Q
Two objects needed ndash quantity possessed by the system
Magnitude EP = qV
EP = kQqr
Units J
Type scalar (+-)
Sign use signs of Q and q
One object needed ndash property of that one object
Magnitude E = Fq
E = kQr2
Units NC
Type vector
Direction away from positive towards negative
Sign donrsquot use when calculating ndash check frame of reference
F = 0 where E = 0 EP = 0 where V = 0
IB 12
11
DO 1 a) Calculate the net electric field at each spot (A and B)
b) Calculate the net electric force on a proton placed at each spot
DO 2 a) Calculate the net electric potential at each spot (A and B)
b) Calculate the electric potential energy of a proton placed at each spot
IB 12
12
Electric Potential and Conductors
For a hollow or solid conductor
1 all the charge resides on the outside surface
2 the electric field is zero everywhere within
3 the external electric field acts as if all the charge is concentrated at the center
4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance
Elec
tric
Fiel
d St
reng
th
Value at surface = kQr2
radius
Graphs for a spherical conductor
Distance
Elec
tric
Pote
ntia
l
radius
DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC
a) What is the electric field at the center of the sphere
b) What is the electric field at the surface of the sphere
c) What is the electric field at a distance of 075 m from the surface of the sphere
d) What is the electric potential at the surface of the sphere
e) What is the electric potential at the center of the sphere
f) What is the electric potential at a distance of 075 m from the surface of the sphere
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
3
The Principle of Superposition
The net electric force acting on a charged particle is the vector sum of all the electric forces acting on it
DO 1 Determine the net electrostatic force on charge q1 as shown below
DO 2 Where can a third charge of +10 microC be placed so that the net force acting on it is zero
DO 3 Three point charges of -20 microC are arranged as shown Determine the magnitude and direction of the net force on charge q1
IB 12
4
Electric Field
Electric field a region in space surrounding a charged object in which a second charged object experiences an electric force
Test charge a small positive charge used to test an electric field
Electric Field Diagrams (DO ALL 7)1 Positively charged sphere 2 Positive point charge 3 Negative point charge
Radial Field field lines are extensions of radii
4 Two positive charges 5 Two negative charges 6 Two unlike charges
Properties of Electric Field Lines
1 Never cross
2 Show the direction of force on a small positive test charge
3 Out of positive into negative
4 Direction of electric field is tangent to the field lines
5 Density of field lines is proportional to field strength (density = intensity)
6 Perpendicular to surface
7 Most intense near sharp points
7 Oppositely charged parallel plates
Edge Effect bowing of field lines at edges
Uniform Field field has same intensity at all spots
IB 12
5
Electric Field Strength (Intensity) electric force exerted per unit charge on a small positive test charge
Electric Field Strength
Units NC
Electric Field Electric Field for a Point Charge
Point Charge Spherical Conductor
DO 1 a) Find the magnitude and direction of the electric field at a spot 0028 meter away from a sphere whose charge is +354 microcoulombs and whose radius is 060 centimeters
b) Find the magnitude and direction of the electric force acting on a -702 nC charge placed at this spot
c) Find the electric field strength at the surface of the sphere
DO 2 a) Find the magnitude and direction of the gravitational field at an altitude of 100 km above the surface of the Earth
b) Find the magnitude and direction of the gravitational force exerted on a 60 kg bowling ball placed at this spot
c) Find the gravitational field strength at the surface of the Earth
Electric Force
Units N
IB 12
6
DO 3 a) Find the magnitude and direction of the net electric field halfway between the two charges shown below
b) Determine the electric force on a proton placed at this spot
DO 4 Two charged objects A and B each contribute as follows to the net electric field at point P EA = 300 NC directed to the right
and EB = 200 NC directed downward What is the net electric field at P
DO 5 a) Two positive point charges q1 = +16 C and q2 = +40 C are separated in a vacuum by a distance of 30 m Find the
spot on the line between the charges where the net electric field is zero
IB 12
7
DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC
a) Describe the motion of the proton
b) Write an expression for the acceleration of the proton
c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate
DO 7 A particle is shot with an initial speed through the two parallel plates as shown
a) Sketch and describe the path it will take if it is a proton an electron or a neutron
b) Which particle will experience a greater force
c) Which particle will experience a greater acceleration
d) Which particle will experience a greater displacement
DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude
IB 12
8
Electric Potential Energy
Gravitational Potential Energy (EP)
Base level where EP = 0
High amount of EP
Low amount of EP
Reason for EP
1 Test object has mass (test mass = m)
2 Test mass is in a gravitational field (g) caused by larger object (M)
3 Larger object exerts a gravitational force on test mass (Fg = mg)
4 Test mass has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Gravitational potential energyEP = mgh W = ΔEP = mg Δh
Electric Potential Energy (EP)
High amount of EP
Low amount of EP
Reason for EP
1 Test object has charge (test charge = +q)
2 Test charge is in an electric field caused by larger object (Q)
3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Electric potential energyEP = Eq hW = ΔEP = Eq Δh
Base level where EP = 0
Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field
EP = 0(Work done by field)
Derivation for Point Charges
Electric Potential Energy due to a point charge
Formula Units
J
Type
scalar
IB 12
9
Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field
Electric Potential due to a point charge
Formula
Units
JC= volts(V)
Type
scalar
ABHigher potential Lower potential
Zero potential
AB
Lower potential Higher potentialZero potential
DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge
b) How much potential energy will an electron have if it is at this spot
c What is the potential where a proton is placed 096 m from a -12 nC charge
IB 12
10
Point Charges
+Q +Q +Q +Q
Electric Force Electric Field Electric Potential Energy Electric Potential
Two objects needed ndash interaction between the two
Magnitude F = Eq
F = kQqr2
Units N
Type vector
Direction likes repel unlikes attract
Sign donrsquot use when calculating ndash check frame of reference
One object needed ndash property of the field
Magnitude V = EPq
V = kQr
Units JC
Type scalar (+-)
Sign use sign of Q
Two objects needed ndash quantity possessed by the system
Magnitude EP = qV
EP = kQqr
Units J
Type scalar (+-)
Sign use signs of Q and q
One object needed ndash property of that one object
Magnitude E = Fq
E = kQr2
Units NC
Type vector
Direction away from positive towards negative
Sign donrsquot use when calculating ndash check frame of reference
F = 0 where E = 0 EP = 0 where V = 0
IB 12
11
DO 1 a) Calculate the net electric field at each spot (A and B)
b) Calculate the net electric force on a proton placed at each spot
DO 2 a) Calculate the net electric potential at each spot (A and B)
b) Calculate the electric potential energy of a proton placed at each spot
IB 12
12
Electric Potential and Conductors
For a hollow or solid conductor
1 all the charge resides on the outside surface
2 the electric field is zero everywhere within
3 the external electric field acts as if all the charge is concentrated at the center
4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance
Elec
tric
Fiel
d St
reng
th
Value at surface = kQr2
radius
Graphs for a spherical conductor
Distance
Elec
tric
Pote
ntia
l
radius
DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC
a) What is the electric field at the center of the sphere
b) What is the electric field at the surface of the sphere
c) What is the electric field at a distance of 075 m from the surface of the sphere
d) What is the electric potential at the surface of the sphere
e) What is the electric potential at the center of the sphere
f) What is the electric potential at a distance of 075 m from the surface of the sphere
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
4
Electric Field
Electric field a region in space surrounding a charged object in which a second charged object experiences an electric force
Test charge a small positive charge used to test an electric field
Electric Field Diagrams (DO ALL 7)1 Positively charged sphere 2 Positive point charge 3 Negative point charge
Radial Field field lines are extensions of radii
4 Two positive charges 5 Two negative charges 6 Two unlike charges
Properties of Electric Field Lines
1 Never cross
2 Show the direction of force on a small positive test charge
3 Out of positive into negative
4 Direction of electric field is tangent to the field lines
5 Density of field lines is proportional to field strength (density = intensity)
6 Perpendicular to surface
7 Most intense near sharp points
7 Oppositely charged parallel plates
Edge Effect bowing of field lines at edges
Uniform Field field has same intensity at all spots
IB 12
5
Electric Field Strength (Intensity) electric force exerted per unit charge on a small positive test charge
Electric Field Strength
Units NC
Electric Field Electric Field for a Point Charge
Point Charge Spherical Conductor
DO 1 a) Find the magnitude and direction of the electric field at a spot 0028 meter away from a sphere whose charge is +354 microcoulombs and whose radius is 060 centimeters
b) Find the magnitude and direction of the electric force acting on a -702 nC charge placed at this spot
c) Find the electric field strength at the surface of the sphere
DO 2 a) Find the magnitude and direction of the gravitational field at an altitude of 100 km above the surface of the Earth
b) Find the magnitude and direction of the gravitational force exerted on a 60 kg bowling ball placed at this spot
c) Find the gravitational field strength at the surface of the Earth
Electric Force
Units N
IB 12
6
DO 3 a) Find the magnitude and direction of the net electric field halfway between the two charges shown below
b) Determine the electric force on a proton placed at this spot
DO 4 Two charged objects A and B each contribute as follows to the net electric field at point P EA = 300 NC directed to the right
and EB = 200 NC directed downward What is the net electric field at P
DO 5 a) Two positive point charges q1 = +16 C and q2 = +40 C are separated in a vacuum by a distance of 30 m Find the
spot on the line between the charges where the net electric field is zero
IB 12
7
DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC
a) Describe the motion of the proton
b) Write an expression for the acceleration of the proton
c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate
DO 7 A particle is shot with an initial speed through the two parallel plates as shown
a) Sketch and describe the path it will take if it is a proton an electron or a neutron
b) Which particle will experience a greater force
c) Which particle will experience a greater acceleration
d) Which particle will experience a greater displacement
DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude
IB 12
8
Electric Potential Energy
Gravitational Potential Energy (EP)
Base level where EP = 0
High amount of EP
Low amount of EP
Reason for EP
1 Test object has mass (test mass = m)
2 Test mass is in a gravitational field (g) caused by larger object (M)
3 Larger object exerts a gravitational force on test mass (Fg = mg)
4 Test mass has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Gravitational potential energyEP = mgh W = ΔEP = mg Δh
Electric Potential Energy (EP)
High amount of EP
Low amount of EP
Reason for EP
1 Test object has charge (test charge = +q)
2 Test charge is in an electric field caused by larger object (Q)
3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Electric potential energyEP = Eq hW = ΔEP = Eq Δh
Base level where EP = 0
Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field
EP = 0(Work done by field)
Derivation for Point Charges
Electric Potential Energy due to a point charge
Formula Units
J
Type
scalar
IB 12
9
Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field
Electric Potential due to a point charge
Formula
Units
JC= volts(V)
Type
scalar
ABHigher potential Lower potential
Zero potential
AB
Lower potential Higher potentialZero potential
DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge
b) How much potential energy will an electron have if it is at this spot
c What is the potential where a proton is placed 096 m from a -12 nC charge
IB 12
10
Point Charges
+Q +Q +Q +Q
Electric Force Electric Field Electric Potential Energy Electric Potential
Two objects needed ndash interaction between the two
Magnitude F = Eq
F = kQqr2
Units N
Type vector
Direction likes repel unlikes attract
Sign donrsquot use when calculating ndash check frame of reference
One object needed ndash property of the field
Magnitude V = EPq
V = kQr
Units JC
Type scalar (+-)
Sign use sign of Q
Two objects needed ndash quantity possessed by the system
Magnitude EP = qV
EP = kQqr
Units J
Type scalar (+-)
Sign use signs of Q and q
One object needed ndash property of that one object
Magnitude E = Fq
E = kQr2
Units NC
Type vector
Direction away from positive towards negative
Sign donrsquot use when calculating ndash check frame of reference
F = 0 where E = 0 EP = 0 where V = 0
IB 12
11
DO 1 a) Calculate the net electric field at each spot (A and B)
b) Calculate the net electric force on a proton placed at each spot
DO 2 a) Calculate the net electric potential at each spot (A and B)
b) Calculate the electric potential energy of a proton placed at each spot
IB 12
12
Electric Potential and Conductors
For a hollow or solid conductor
1 all the charge resides on the outside surface
2 the electric field is zero everywhere within
3 the external electric field acts as if all the charge is concentrated at the center
4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance
Elec
tric
Fiel
d St
reng
th
Value at surface = kQr2
radius
Graphs for a spherical conductor
Distance
Elec
tric
Pote
ntia
l
radius
DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC
a) What is the electric field at the center of the sphere
b) What is the electric field at the surface of the sphere
c) What is the electric field at a distance of 075 m from the surface of the sphere
d) What is the electric potential at the surface of the sphere
e) What is the electric potential at the center of the sphere
f) What is the electric potential at a distance of 075 m from the surface of the sphere
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
5
Electric Field Strength (Intensity) electric force exerted per unit charge on a small positive test charge
Electric Field Strength
Units NC
Electric Field Electric Field for a Point Charge
Point Charge Spherical Conductor
DO 1 a) Find the magnitude and direction of the electric field at a spot 0028 meter away from a sphere whose charge is +354 microcoulombs and whose radius is 060 centimeters
b) Find the magnitude and direction of the electric force acting on a -702 nC charge placed at this spot
c) Find the electric field strength at the surface of the sphere
DO 2 a) Find the magnitude and direction of the gravitational field at an altitude of 100 km above the surface of the Earth
b) Find the magnitude and direction of the gravitational force exerted on a 60 kg bowling ball placed at this spot
c) Find the gravitational field strength at the surface of the Earth
Electric Force
Units N
IB 12
6
DO 3 a) Find the magnitude and direction of the net electric field halfway between the two charges shown below
b) Determine the electric force on a proton placed at this spot
DO 4 Two charged objects A and B each contribute as follows to the net electric field at point P EA = 300 NC directed to the right
and EB = 200 NC directed downward What is the net electric field at P
DO 5 a) Two positive point charges q1 = +16 C and q2 = +40 C are separated in a vacuum by a distance of 30 m Find the
spot on the line between the charges where the net electric field is zero
IB 12
7
DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC
a) Describe the motion of the proton
b) Write an expression for the acceleration of the proton
c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate
DO 7 A particle is shot with an initial speed through the two parallel plates as shown
a) Sketch and describe the path it will take if it is a proton an electron or a neutron
b) Which particle will experience a greater force
c) Which particle will experience a greater acceleration
d) Which particle will experience a greater displacement
DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude
IB 12
8
Electric Potential Energy
Gravitational Potential Energy (EP)
Base level where EP = 0
High amount of EP
Low amount of EP
Reason for EP
1 Test object has mass (test mass = m)
2 Test mass is in a gravitational field (g) caused by larger object (M)
3 Larger object exerts a gravitational force on test mass (Fg = mg)
4 Test mass has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Gravitational potential energyEP = mgh W = ΔEP = mg Δh
Electric Potential Energy (EP)
High amount of EP
Low amount of EP
Reason for EP
1 Test object has charge (test charge = +q)
2 Test charge is in an electric field caused by larger object (Q)
3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Electric potential energyEP = Eq hW = ΔEP = Eq Δh
Base level where EP = 0
Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field
EP = 0(Work done by field)
Derivation for Point Charges
Electric Potential Energy due to a point charge
Formula Units
J
Type
scalar
IB 12
9
Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field
Electric Potential due to a point charge
Formula
Units
JC= volts(V)
Type
scalar
ABHigher potential Lower potential
Zero potential
AB
Lower potential Higher potentialZero potential
DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge
b) How much potential energy will an electron have if it is at this spot
c What is the potential where a proton is placed 096 m from a -12 nC charge
IB 12
10
Point Charges
+Q +Q +Q +Q
Electric Force Electric Field Electric Potential Energy Electric Potential
Two objects needed ndash interaction between the two
Magnitude F = Eq
F = kQqr2
Units N
Type vector
Direction likes repel unlikes attract
Sign donrsquot use when calculating ndash check frame of reference
One object needed ndash property of the field
Magnitude V = EPq
V = kQr
Units JC
Type scalar (+-)
Sign use sign of Q
Two objects needed ndash quantity possessed by the system
Magnitude EP = qV
EP = kQqr
Units J
Type scalar (+-)
Sign use signs of Q and q
One object needed ndash property of that one object
Magnitude E = Fq
E = kQr2
Units NC
Type vector
Direction away from positive towards negative
Sign donrsquot use when calculating ndash check frame of reference
F = 0 where E = 0 EP = 0 where V = 0
IB 12
11
DO 1 a) Calculate the net electric field at each spot (A and B)
b) Calculate the net electric force on a proton placed at each spot
DO 2 a) Calculate the net electric potential at each spot (A and B)
b) Calculate the electric potential energy of a proton placed at each spot
IB 12
12
Electric Potential and Conductors
For a hollow or solid conductor
1 all the charge resides on the outside surface
2 the electric field is zero everywhere within
3 the external electric field acts as if all the charge is concentrated at the center
4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance
Elec
tric
Fiel
d St
reng
th
Value at surface = kQr2
radius
Graphs for a spherical conductor
Distance
Elec
tric
Pote
ntia
l
radius
DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC
a) What is the electric field at the center of the sphere
b) What is the electric field at the surface of the sphere
c) What is the electric field at a distance of 075 m from the surface of the sphere
d) What is the electric potential at the surface of the sphere
e) What is the electric potential at the center of the sphere
f) What is the electric potential at a distance of 075 m from the surface of the sphere
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
6
DO 3 a) Find the magnitude and direction of the net electric field halfway between the two charges shown below
b) Determine the electric force on a proton placed at this spot
DO 4 Two charged objects A and B each contribute as follows to the net electric field at point P EA = 300 NC directed to the right
and EB = 200 NC directed downward What is the net electric field at P
DO 5 a) Two positive point charges q1 = +16 C and q2 = +40 C are separated in a vacuum by a distance of 30 m Find the
spot on the line between the charges where the net electric field is zero
IB 12
7
DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC
a) Describe the motion of the proton
b) Write an expression for the acceleration of the proton
c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate
DO 7 A particle is shot with an initial speed through the two parallel plates as shown
a) Sketch and describe the path it will take if it is a proton an electron or a neutron
b) Which particle will experience a greater force
c) Which particle will experience a greater acceleration
d) Which particle will experience a greater displacement
DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude
IB 12
8
Electric Potential Energy
Gravitational Potential Energy (EP)
Base level where EP = 0
High amount of EP
Low amount of EP
Reason for EP
1 Test object has mass (test mass = m)
2 Test mass is in a gravitational field (g) caused by larger object (M)
3 Larger object exerts a gravitational force on test mass (Fg = mg)
4 Test mass has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Gravitational potential energyEP = mgh W = ΔEP = mg Δh
Electric Potential Energy (EP)
High amount of EP
Low amount of EP
Reason for EP
1 Test object has charge (test charge = +q)
2 Test charge is in an electric field caused by larger object (Q)
3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Electric potential energyEP = Eq hW = ΔEP = Eq Δh
Base level where EP = 0
Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field
EP = 0(Work done by field)
Derivation for Point Charges
Electric Potential Energy due to a point charge
Formula Units
J
Type
scalar
IB 12
9
Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field
Electric Potential due to a point charge
Formula
Units
JC= volts(V)
Type
scalar
ABHigher potential Lower potential
Zero potential
AB
Lower potential Higher potentialZero potential
DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge
b) How much potential energy will an electron have if it is at this spot
c What is the potential where a proton is placed 096 m from a -12 nC charge
IB 12
10
Point Charges
+Q +Q +Q +Q
Electric Force Electric Field Electric Potential Energy Electric Potential
Two objects needed ndash interaction between the two
Magnitude F = Eq
F = kQqr2
Units N
Type vector
Direction likes repel unlikes attract
Sign donrsquot use when calculating ndash check frame of reference
One object needed ndash property of the field
Magnitude V = EPq
V = kQr
Units JC
Type scalar (+-)
Sign use sign of Q
Two objects needed ndash quantity possessed by the system
Magnitude EP = qV
EP = kQqr
Units J
Type scalar (+-)
Sign use signs of Q and q
One object needed ndash property of that one object
Magnitude E = Fq
E = kQr2
Units NC
Type vector
Direction away from positive towards negative
Sign donrsquot use when calculating ndash check frame of reference
F = 0 where E = 0 EP = 0 where V = 0
IB 12
11
DO 1 a) Calculate the net electric field at each spot (A and B)
b) Calculate the net electric force on a proton placed at each spot
DO 2 a) Calculate the net electric potential at each spot (A and B)
b) Calculate the electric potential energy of a proton placed at each spot
IB 12
12
Electric Potential and Conductors
For a hollow or solid conductor
1 all the charge resides on the outside surface
2 the electric field is zero everywhere within
3 the external electric field acts as if all the charge is concentrated at the center
4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance
Elec
tric
Fiel
d St
reng
th
Value at surface = kQr2
radius
Graphs for a spherical conductor
Distance
Elec
tric
Pote
ntia
l
radius
DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC
a) What is the electric field at the center of the sphere
b) What is the electric field at the surface of the sphere
c) What is the electric field at a distance of 075 m from the surface of the sphere
d) What is the electric potential at the surface of the sphere
e) What is the electric potential at the center of the sphere
f) What is the electric potential at a distance of 075 m from the surface of the sphere
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
7
DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC
a) Describe the motion of the proton
b) Write an expression for the acceleration of the proton
c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate
DO 7 A particle is shot with an initial speed through the two parallel plates as shown
a) Sketch and describe the path it will take if it is a proton an electron or a neutron
b) Which particle will experience a greater force
c) Which particle will experience a greater acceleration
d) Which particle will experience a greater displacement
DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude
IB 12
8
Electric Potential Energy
Gravitational Potential Energy (EP)
Base level where EP = 0
High amount of EP
Low amount of EP
Reason for EP
1 Test object has mass (test mass = m)
2 Test mass is in a gravitational field (g) caused by larger object (M)
3 Larger object exerts a gravitational force on test mass (Fg = mg)
4 Test mass has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Gravitational potential energyEP = mgh W = ΔEP = mg Δh
Electric Potential Energy (EP)
High amount of EP
Low amount of EP
Reason for EP
1 Test object has charge (test charge = +q)
2 Test charge is in an electric field caused by larger object (Q)
3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Electric potential energyEP = Eq hW = ΔEP = Eq Δh
Base level where EP = 0
Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field
EP = 0(Work done by field)
Derivation for Point Charges
Electric Potential Energy due to a point charge
Formula Units
J
Type
scalar
IB 12
9
Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field
Electric Potential due to a point charge
Formula
Units
JC= volts(V)
Type
scalar
ABHigher potential Lower potential
Zero potential
AB
Lower potential Higher potentialZero potential
DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge
b) How much potential energy will an electron have if it is at this spot
c What is the potential where a proton is placed 096 m from a -12 nC charge
IB 12
10
Point Charges
+Q +Q +Q +Q
Electric Force Electric Field Electric Potential Energy Electric Potential
Two objects needed ndash interaction between the two
Magnitude F = Eq
F = kQqr2
Units N
Type vector
Direction likes repel unlikes attract
Sign donrsquot use when calculating ndash check frame of reference
One object needed ndash property of the field
Magnitude V = EPq
V = kQr
Units JC
Type scalar (+-)
Sign use sign of Q
Two objects needed ndash quantity possessed by the system
Magnitude EP = qV
EP = kQqr
Units J
Type scalar (+-)
Sign use signs of Q and q
One object needed ndash property of that one object
Magnitude E = Fq
E = kQr2
Units NC
Type vector
Direction away from positive towards negative
Sign donrsquot use when calculating ndash check frame of reference
F = 0 where E = 0 EP = 0 where V = 0
IB 12
11
DO 1 a) Calculate the net electric field at each spot (A and B)
b) Calculate the net electric force on a proton placed at each spot
DO 2 a) Calculate the net electric potential at each spot (A and B)
b) Calculate the electric potential energy of a proton placed at each spot
IB 12
12
Electric Potential and Conductors
For a hollow or solid conductor
1 all the charge resides on the outside surface
2 the electric field is zero everywhere within
3 the external electric field acts as if all the charge is concentrated at the center
4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance
Elec
tric
Fiel
d St
reng
th
Value at surface = kQr2
radius
Graphs for a spherical conductor
Distance
Elec
tric
Pote
ntia
l
radius
DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC
a) What is the electric field at the center of the sphere
b) What is the electric field at the surface of the sphere
c) What is the electric field at a distance of 075 m from the surface of the sphere
d) What is the electric potential at the surface of the sphere
e) What is the electric potential at the center of the sphere
f) What is the electric potential at a distance of 075 m from the surface of the sphere
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
8
Electric Potential Energy
Gravitational Potential Energy (EP)
Base level where EP = 0
High amount of EP
Low amount of EP
Reason for EP
1 Test object has mass (test mass = m)
2 Test mass is in a gravitational field (g) caused by larger object (M)
3 Larger object exerts a gravitational force on test mass (Fg = mg)
4 Test mass has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Gravitational potential energyEP = mgh W = ΔEP = mg Δh
Electric Potential Energy (EP)
High amount of EP
Low amount of EP
Reason for EP
1 Test object has charge (test charge = +q)
2 Test charge is in an electric field caused by larger object (Q)
3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force
5 Work done moving object between two positions is path independent
Electric potential energyEP = Eq hW = ΔEP = Eq Δh
Base level where EP = 0
Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field
EP = 0(Work done by field)
Derivation for Point Charges
Electric Potential Energy due to a point charge
Formula Units
J
Type
scalar
IB 12
9
Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field
Electric Potential due to a point charge
Formula
Units
JC= volts(V)
Type
scalar
ABHigher potential Lower potential
Zero potential
AB
Lower potential Higher potentialZero potential
DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge
b) How much potential energy will an electron have if it is at this spot
c What is the potential where a proton is placed 096 m from a -12 nC charge
IB 12
10
Point Charges
+Q +Q +Q +Q
Electric Force Electric Field Electric Potential Energy Electric Potential
Two objects needed ndash interaction between the two
Magnitude F = Eq
F = kQqr2
Units N
Type vector
Direction likes repel unlikes attract
Sign donrsquot use when calculating ndash check frame of reference
One object needed ndash property of the field
Magnitude V = EPq
V = kQr
Units JC
Type scalar (+-)
Sign use sign of Q
Two objects needed ndash quantity possessed by the system
Magnitude EP = qV
EP = kQqr
Units J
Type scalar (+-)
Sign use signs of Q and q
One object needed ndash property of that one object
Magnitude E = Fq
E = kQr2
Units NC
Type vector
Direction away from positive towards negative
Sign donrsquot use when calculating ndash check frame of reference
F = 0 where E = 0 EP = 0 where V = 0
IB 12
11
DO 1 a) Calculate the net electric field at each spot (A and B)
b) Calculate the net electric force on a proton placed at each spot
DO 2 a) Calculate the net electric potential at each spot (A and B)
b) Calculate the electric potential energy of a proton placed at each spot
IB 12
12
Electric Potential and Conductors
For a hollow or solid conductor
1 all the charge resides on the outside surface
2 the electric field is zero everywhere within
3 the external electric field acts as if all the charge is concentrated at the center
4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance
Elec
tric
Fiel
d St
reng
th
Value at surface = kQr2
radius
Graphs for a spherical conductor
Distance
Elec
tric
Pote
ntia
l
radius
DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC
a) What is the electric field at the center of the sphere
b) What is the electric field at the surface of the sphere
c) What is the electric field at a distance of 075 m from the surface of the sphere
d) What is the electric potential at the surface of the sphere
e) What is the electric potential at the center of the sphere
f) What is the electric potential at a distance of 075 m from the surface of the sphere
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
9
Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field
Electric Potential due to a point charge
Formula
Units
JC= volts(V)
Type
scalar
ABHigher potential Lower potential
Zero potential
AB
Lower potential Higher potentialZero potential
DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge
b) How much potential energy will an electron have if it is at this spot
c What is the potential where a proton is placed 096 m from a -12 nC charge
IB 12
10
Point Charges
+Q +Q +Q +Q
Electric Force Electric Field Electric Potential Energy Electric Potential
Two objects needed ndash interaction between the two
Magnitude F = Eq
F = kQqr2
Units N
Type vector
Direction likes repel unlikes attract
Sign donrsquot use when calculating ndash check frame of reference
One object needed ndash property of the field
Magnitude V = EPq
V = kQr
Units JC
Type scalar (+-)
Sign use sign of Q
Two objects needed ndash quantity possessed by the system
Magnitude EP = qV
EP = kQqr
Units J
Type scalar (+-)
Sign use signs of Q and q
One object needed ndash property of that one object
Magnitude E = Fq
E = kQr2
Units NC
Type vector
Direction away from positive towards negative
Sign donrsquot use when calculating ndash check frame of reference
F = 0 where E = 0 EP = 0 where V = 0
IB 12
11
DO 1 a) Calculate the net electric field at each spot (A and B)
b) Calculate the net electric force on a proton placed at each spot
DO 2 a) Calculate the net electric potential at each spot (A and B)
b) Calculate the electric potential energy of a proton placed at each spot
IB 12
12
Electric Potential and Conductors
For a hollow or solid conductor
1 all the charge resides on the outside surface
2 the electric field is zero everywhere within
3 the external electric field acts as if all the charge is concentrated at the center
4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance
Elec
tric
Fiel
d St
reng
th
Value at surface = kQr2
radius
Graphs for a spherical conductor
Distance
Elec
tric
Pote
ntia
l
radius
DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC
a) What is the electric field at the center of the sphere
b) What is the electric field at the surface of the sphere
c) What is the electric field at a distance of 075 m from the surface of the sphere
d) What is the electric potential at the surface of the sphere
e) What is the electric potential at the center of the sphere
f) What is the electric potential at a distance of 075 m from the surface of the sphere
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
10
Point Charges
+Q +Q +Q +Q
Electric Force Electric Field Electric Potential Energy Electric Potential
Two objects needed ndash interaction between the two
Magnitude F = Eq
F = kQqr2
Units N
Type vector
Direction likes repel unlikes attract
Sign donrsquot use when calculating ndash check frame of reference
One object needed ndash property of the field
Magnitude V = EPq
V = kQr
Units JC
Type scalar (+-)
Sign use sign of Q
Two objects needed ndash quantity possessed by the system
Magnitude EP = qV
EP = kQqr
Units J
Type scalar (+-)
Sign use signs of Q and q
One object needed ndash property of that one object
Magnitude E = Fq
E = kQr2
Units NC
Type vector
Direction away from positive towards negative
Sign donrsquot use when calculating ndash check frame of reference
F = 0 where E = 0 EP = 0 where V = 0
IB 12
11
DO 1 a) Calculate the net electric field at each spot (A and B)
b) Calculate the net electric force on a proton placed at each spot
DO 2 a) Calculate the net electric potential at each spot (A and B)
b) Calculate the electric potential energy of a proton placed at each spot
IB 12
12
Electric Potential and Conductors
For a hollow or solid conductor
1 all the charge resides on the outside surface
2 the electric field is zero everywhere within
3 the external electric field acts as if all the charge is concentrated at the center
4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance
Elec
tric
Fiel
d St
reng
th
Value at surface = kQr2
radius
Graphs for a spherical conductor
Distance
Elec
tric
Pote
ntia
l
radius
DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC
a) What is the electric field at the center of the sphere
b) What is the electric field at the surface of the sphere
c) What is the electric field at a distance of 075 m from the surface of the sphere
d) What is the electric potential at the surface of the sphere
e) What is the electric potential at the center of the sphere
f) What is the electric potential at a distance of 075 m from the surface of the sphere
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
11
DO 1 a) Calculate the net electric field at each spot (A and B)
b) Calculate the net electric force on a proton placed at each spot
DO 2 a) Calculate the net electric potential at each spot (A and B)
b) Calculate the electric potential energy of a proton placed at each spot
IB 12
12
Electric Potential and Conductors
For a hollow or solid conductor
1 all the charge resides on the outside surface
2 the electric field is zero everywhere within
3 the external electric field acts as if all the charge is concentrated at the center
4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance
Elec
tric
Fiel
d St
reng
th
Value at surface = kQr2
radius
Graphs for a spherical conductor
Distance
Elec
tric
Pote
ntia
l
radius
DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC
a) What is the electric field at the center of the sphere
b) What is the electric field at the surface of the sphere
c) What is the electric field at a distance of 075 m from the surface of the sphere
d) What is the electric potential at the surface of the sphere
e) What is the electric potential at the center of the sphere
f) What is the electric potential at a distance of 075 m from the surface of the sphere
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
12
Electric Potential and Conductors
For a hollow or solid conductor
1 all the charge resides on the outside surface
2 the electric field is zero everywhere within
3 the external electric field acts as if all the charge is concentrated at the center
4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance
Elec
tric
Fiel
d St
reng
th
Value at surface = kQr2
radius
Graphs for a spherical conductor
Distance
Elec
tric
Pote
ntia
l
radius
DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC
a) What is the electric field at the center of the sphere
b) What is the electric field at the surface of the sphere
c) What is the electric field at a distance of 075 m from the surface of the sphere
d) What is the electric potential at the surface of the sphere
e) What is the electric potential at the center of the sphere
f) What is the electric potential at a distance of 075 m from the surface of the sphere
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
13
Equipotential Surfaces
Equipotential surface a surface on which the electric potential is the same everywhere
1 Locate points that are at the same electric potential around each of the point charges shown
2 Sketch in the electric field lines for each point charge
3 What is the relationship between the electric field lines and the equipotential surfaces
PerpendicularField lines point in direction
of decreasing potential
Electric Potential Gradient
The electric field strength is the negative of the electric potential gradient
Formula
Units Nc or Vm
For each electric field shown sketch in equipotential surfaces
Sketch in equipotential surfaces for the two configurations of point charges below
httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
14
Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field
Electric Potential Difference
Formula
Units JC = V
High and Low Potential
DO 1 a) Which plate is at a higher electric potential
b) Which plate is at a lower electric potential
c) What is the electric potential of each plate
d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials
e) Where will a proton have the most electric potential energy
an electron a neutron an alpha particle
DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts
b) Calculate the strength of the electric field
a) Calculate how fast the electron strikes the positive plate
Formula
qV = frac12 mv2
Ve = frac12 mv2
Formula
E = -ΔVΔxE = Vd
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron
IB 12
15
DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)
The Electronvolt
Electronvolt energy gained by an electron moving through a potential difference of one volt
ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV
ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J
Therefore 1 eV = 160 x 10-19 J
Derivation
DO 1 How much energy is gained by a proton moving through a potential difference of 150 V
DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this
DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron