Lecture 10 Chapter 15 Chapter 16 Chapter 17 Chapter 18.
-
Upload
primrose-hutchinson -
Category
Documents
-
view
231 -
download
4
Transcript of Lecture 10 Chapter 15 Chapter 16 Chapter 17 Chapter 18.
Lecture 10 Chapter 15 Chapter 16 Chapter 17 Chapter 18
Fig. 15-CO, p.497
First Observations – Greeks Observed electric and magnetic
phenomena as early as 700 BC Found that amber, when rubbed,
became electrified and attracted pieces of straw or feathers
Also discovered magnetic forces by observing magnetite attracting iron
Fig. 15-1b, p.498
Fig. 15-2, p.499
Fig. 15-3a, p.499
Fig. 15-1, p.498
Properties of Charge, final Charge is quantized
All charge is a multiple of a fundamental unit of charge, symbolized by e
Quarks are the exception Electrons have a charge of –e Protons have a charge of +e The SI unit of charge is the Coulomb (C)
e = 1.6 x 10-19 C
Conductors Conductors are materials in which
the electric charges move freely in response to an electric force Copper, aluminum and silver are good
conductors When a conductor is charged in a
small region, the charge readily distributes itself over the entire surface of the material
Insulators Insulators are materials in which
electric charges do not move freely Glass and rubber are examples of
insulators When insulators are charged by
rubbing, only the rubbed area becomes charged
There is no tendency for the charge to move into other regions of the material
Semiconductors The characteristics of
semiconductors are between those of insulators and conductors
Silicon and germanium are examples of semiconductors
Charging by Conduction A charged object (the rod)
is placed in contact with another object (the sphere)
Some electrons on the rod can move to the sphere
When the rod is removed, the sphere is left with a charge
The object being charged is always left with a charge having the same sign as the object doing the charging
Fig. 15-5a, p.501
Fig. 15-5b, p.501
Coulomb’s Law Coulomb shows that an electrical force
has the following properties: It is along the line joining the two particles
and inversely proportional to the square of the separation distance, r, between them
It is proportional to the product of the magnitudes of the charges, |q1|and |q2|on the two particles
It is attractive if the charges are of opposite signs and repulsive if the charges have the same signs
Coulomb’s Law, cont. Mathematically,
ke is called the Coulomb Constant ke = 8.9875 x 109 N m2/C2
Typical charges can be in the µC range Remember, Coulombs must be used in the
equation Remember that force is a vector quantity Applies only to point charges
Coulomb's law
2
21e r
qqkF
Characteristics of Particles
Fig. 15-6a, p.502
Fig. 15-6b, p.502
Electrical Forces are Field Forces This is the second example of a field
force Gravity was the first
Remember, with a field force, the force is exerted by one object on another object even though there is no physical contact between them
There are some important similarities and differences between electrical and gravitational forces
The Superposition Principle The resultant force on any one
charge equals the vector sum of the forces exerted by the other individual charges that are present. Remember to add the forces as
vectors
Fig. 15-8, p.504
Electrical Forces are Field Forces This is the second example of a field
force Gravity was the first
Remember, with a field force, the force is exerted by one object on another object even though there is no physical contact between them
There are some important similarities and differences between electrical and gravitational forces
Electrical Force Compared to Gravitational Force Both are inverse square laws The mathematical form of both laws is
the same Masses replaced by charges
Electrical forces can be either attractive or repulsive
Gravitational forces are always attractive Electrostatic force is stronger than the
gravitational force
The Superposition Principle The resultant force on any one
charge equals the vector sum of the forces exerted by the other individual charges that are present. Remember to add the forces as
vectors
Fig. 15-8, p.504
Superposition Principle Example
The force exerted by q1 on q3 is
The force exerted by q2 on q3 is
The total force exerted on q3 is the vector sum of
and
13F
13F
23F
23F
Fig. 15-9, p.505
Electric Field
Mathematically,
SI units are N / C Use this for the magnitude of the field The electric field is a vector quantity The direction of the field is defined to be
the direction of the electric force that would be exerted on a small positive test charge placed at that point
2e
o
k Qq r
F
E
Direction of Electric Field The electric field
produced by a negative charge is directed toward the charge A positive test
charge would be attracted to the negative source charge
Electric Field Lines A convenient aid for visualizing
electric field patterns is to draw lines pointing in the direction of the field vector at any point
These are called electric field lines and were introduced by Michael Faraday
Fig. 15-13a, p.510
Fig. 15-13b, p.510
Electric Field Line Patterns An electric dipole
consists of two equal and opposite charges
The high density of lines between the charges indicates the strong electric field in this region
Electric Field Line Patterns Two equal but like point
charges At a great distance from
the charges, the field would be approximately that of a single charge of 2q
The bulging out of the field lines between the charges indicates the repulsion between the charges
The low field lines between the charges indicates a weak field in this region
Electric Field Patterns Unequal and
unlike charges Note that two
lines leave the +2q charge for each line that terminates on -q
Fig. 15-18a, p.513
Fig. 15-18b, p.513
Van de GraaffGenerator An electrostatic generator
designed and built by Robert J. Van de Graaff in 1929
Charge is transferred to the dome by means of a rotating belt
Eventually an electrostatic discharge takes place
Electrical Potential Energy of Two Charges
V1 is the electric potential due to q1 at some point P
The work required to bring q2 from infinity to P without acceleration is q2V1
This work is equal to the potential energy of the two particle system
r
qqkVqPE 21e12
The Electron Volt The electron volt (eV) is defined as the
energy that an electron gains when accelerated through a potential difference of 1 V Electrons in normal atoms have energies of
10’s of eV Excited electrons have energies of 1000’s of
eV High energy gamma rays have energies of
millions of eV 1 eV = 1.6 x 10-19 J
Equipotential Surfaces An equipotential surface is a
surface on which all points are at the same potential No work is required to move a charge
at a constant speed on an equipotential surface
The electric field at every point on an equipotential surface is perpendicular to the surface
Equipotentials and Electric Fields Lines – Positive Charge
The equipotentials for a point charge are a family of spheres centered on the point charge
The field lines are perpendicular to the electric potential at all points
Equipotentials and Electric Fields Lines – Dipole Equipotential lines
are shown in blue Electric field lines
are shown in red The field lines are
perpendicular to the equipotential lines at all points
Capacitance, cont
Units: Farad (F) 1 F = 1 C / V A Farad is very large
Often will see µF or pF
V
QC
Parallel-Plate Capacitor The capacitance of a device
depends on the geometric arrangement of the conductors
For a parallel-plate capacitor whose plates are separated by air:
d
AC o
Parallel-Plate Capacitor, Example
The capacitor consists of two parallel plates
Each have area A They are separated by a
distance d The plates carry equal and
opposite charges When connected to the
battery, charge is pulled off one plate and transferred to the other plate
The transfer stops when Vcap = Vbattery
Demo 2
Capacitors in Parallel The total charge is
equal to the sum of the charges on the capacitors
Qtotal = Q1 + Q2
The potential difference across the capacitors is the same
And each is equal to the voltage of the battery
Fig. 16-19, p.551
Fig. 16-20, p.552
Fig. P16-34, p.564
Fig. 16-21, p.553
Energy Stored in a Capacitor Energy stored = ½ Q ΔV From the definition of capacitance,
this can be rewritten in different forms
C2
QVC
2
1VQ
2
1Energy
22
Dielectric Strength For any given plate separation,
there is a maximum electric field that can be produced in the dielectric before it breaks down and begins to conduct
This maximum electric field is called the dielectric strength
Table 16-1, p.557
Electric Current Whenever electric charges of like signs
move, an electric current is said to exist The current is the rate at which the
charge flows through this surface Look at the charges flowing perpendicularly
to a surface of area A
The SI unit of current is Ampere (A) 1 A = 1 C/s
QI
t
Electric Current, cont The direction of the current is the
direction positive charge would flow This is known as conventional current
direction In a common conductor, such as copper, the
current is due to the motion of the negatively charged electrons
It is common to refer to a moving charge as a mobile charge carrier A charge carrier can be positive or negative
Current and Drift Speed
Charged particles move through a conductor of cross-sectional area A
n is the number of charge carriers per unit volume
n A Δx is the total number of charge carriers
Current and Drift Speed, cont The total charge is the number of
carriers times the charge per carrier, q ΔQ = (n A Δx) q
The drift speed, vd, is the speed at which the carriers move vd = Δx/ Δt
Rewritten: ΔQ = (n A vd Δt) q Finally, current, I = ΔQ/Δt = nqvdA
Current and Drift Speed, final If the conductor is isolated, the
electrons undergo random motion When an electric field is set up in
the conductor, it creates an electric force on the electrons and hence a current
Charge Carrier Motion in a Conductor
The zig-zag black line represents the motion of charge carrier in a conductor
The net drift speed is small
The sharp changes in direction are due to collisions
The net motion of electrons is opposite the direction of the electric field Demo
p.578
Resistance In a conductor, the voltage applied
across the ends of the conductor is proportional to the current through the conductor
The constant of proportionality is the resistance of the conductor
VR
I
Fig. 17-CO, p.568
Resistance, cont Units of resistance are ohms (Ω)
1 Ω = 1 V / A Resistance in a circuit arises due to
collisions between the electrons carrying the current with the fixed atoms inside the conductor
Ohm’s Law Experiments show that for many materials,
including most metals, the resistance remains constant over a wide range of applied voltages or currents
This statement has become known as Ohm’s Law ΔV = I R
Ohm’s Law is an empirical relationship that is valid only for certain materials Materials that obey Ohm’s Law are said to be
ohmic
Resistivity The resistance of an ohmic conductor is
proportional to its length, L, and inversely proportional to its cross-sectional area, A
ρ is the constant of proportionality and is called the resistivity of the material
LR
A
Table 17-1, p.576
Temperature Variation of Resistivity For most metals, resistivity
increases with increasing temperature With a higher temperature, the
metal’s constituent atoms vibrate with increasing amplitude
The electrons find it more difficult to pass through the atoms
Temperature Variation of Resistivity, cont For most metals, resistivity increases
approximately linearly with temperature over a limited temperature range
ρ is the resistivity at some temperature T ρo is the resistivity at some reference
temperature To To is usually taken to be 20° C = 68 ° F is the temperature coefficient of resistivity
)]TT(1[ oo
Temperature Variation of Resistance Since the resistance of a conductor
with uniform cross sectional area is proportional to the resistivity, you can find the effect of temperature on resistance
)]TT(1[RR oo
Electrical Energy and Power, cont The rate at which the energy is lost
is the power
From Ohm’s Law, alternate forms of power are
QV I V
t
22 V
I RR
Electrical Energy and Power, final The SI unit of power is Watt (W)
I must be in Amperes, R in ohms and V in Volts
The unit of energy used by electric companies is the kilowatt-hour This is defined in terms of the unit of
power and the amount of time it is supplied
1 kWh = 3.60 x 106 J
Fig. Q18-13, p.616
More About the Junction Rule I1 = I2 + I3 From
Conservation of Charge
Diagram b shows a mechanical analog
RC Circuits A direct current circuit may contain
capacitors and resistors, the current will vary with time
When the circuit is completed, the capacitor starts to charge
The capacitor continues to charge until it reaches its maximum charge (Q = Cε)
Once the capacitor is fully charged, the current in the circuit is zero
Charging Capacitor in an RC Circuit
The charge on the capacitor varies with time
q = Q(1 – e-t/RC) The time constant,
=RC The time constant
represents the time required for the charge to increase from zero to 63.2% of its maximum
Notes on Time Constant In a circuit with a large time
constant, the capacitor charges very slowly
The capacitor charges very quickly if there is a small time constant
After t = 10 , the capacitor is over 99.99% charged
Household Circuits The utility company
distributes electric power to individual houses with a pair of wires
Electrical devices in the house are connected in parallel with those wires
The potential difference between the wires is about 120V
Effects of Various Currents 5 mA or less
Can cause a sensation of shock Generally little or no damage
10 mA Hand muscles contract May be unable to let go a of live wire
100 mA If passes through the body for just a few
seconds, can be fatal