Monday, January 14, 2008 Charge and Polarization.

Monday, January 14, 2008

Charge and Polarization

Demonstration #1

1. Demonstrate how you can pick up the tissue without touching it in any way with your body.

2. What is occurring on the atomic level that lets you do this?

The atom

The atom has positive charge in the nucleus, located in the protons. The positive charge cannot move from the atom unless there is a nuclear reaction.

The atom has negative charge in the electron cloud on the outside of the atom. Electrons can move from atom to atom without all that much difficulty.

Question

You charge the balloon by rubbing it on hair or on a sweater, and the balloon becomes negative. How can it pick up a neutral tissue?

This is an electroscope

Pole

Vanes

The electroscope is made from a metal or other conductor, and may be contained within a flask.

The vanes are free to move.

Demonstration #2

1. Rub the black rod with the fur. Bring the rod toward the pole of the electroscope. What happens to the vanes?

2. Come up with an atomic-level explanation for your observations.

Demonstration #3

1. Rub the glass rod with the silk. Bring the rod toward the pole of the electroscope. What happens to the vanes?

2. Come up with an atomic-level explanation for your observations.

Demonstration #4

1. What happens when your touch the electroscope with the glass rod?

Charge

Charge comes in two forms, which Ben Franklin designated as positive (+) and negative(–).

Charge is quantized. The smallest possible stable charge, which we

designate as e, is the magnitude of the charge on 1 electron or 1 proton.

We say a proton has charge of e, and an electron has a charge of –e.

e is referred to as the “elementary” charge. e = 1.602 10-19 Coulombs. The coulomb is the SI unit of charge.

Sample ProblemA certain static discharge delivers -0.5 Coulombs of electrical charge.

How many electrons are in this discharge?

Sample Problem1. How much positive charge resides in two moles of hydrogen

gas (H2)?

2. How much negative charge?

3. How much net charge?

Sample ProblemThe total charge of a system composed of 1800 particles,

all of which are protons or electrons, is 31x10-18 C.• How many protons are in the system?

• How many electrons are in the system?

Tuesday, January 15, 2008

Coulomb’s Law and Electrical Force

Electric Force

Charges exert forces on each other.Like charges (two positives, or two

negatives) repel each other, resulting in a repulsive force.

Opposite charges (a positive and a negative) attract each other, resulting in an attractive force.

Coulomb’s Law – form 1

Coulomb’s law tells us how the magnitude of the force between two particles varies with their charge and with the distance between them.

k = 8.99 109 N m2 / C2

q1, q2 are charges (C) r is distance between the charges (m) F is force (N)

Coulomb’s law applies directly only to spherically symmetric charges.

1 22

kq qF

r

Coulomb’s Law – form 2

Sometimes you see Coulomb’s Law written in a slightly different form

o = 8.85 10-12 C2/ N m2 q1, q2 are charges (C) r is distance between the charges (m) F is force (N)

This version is theoretically derived and less practical that form 1

1 22

0

1

4

q qF

r

Spherically Symmetric Forces

Newton’s Law of Gravity

Coulomb’s Law

1 22G

GmmF

r

1 22E

kq qF

r

Sample ProblemA point charge of positive 12.0 μC experiences an attractive force of 51 mN

when it is placed 15 cm from another point charge. What is the other charge?

Sample ProblemCalculate the mass of ball B, which is suspended in midair.

A

B

qA = 1.50 nC

qB = -0.50 nC

1.3 m

Superposition

Electrical force, like all forces, is a vector quantity.

If a charge is subjected to forces from more than one other charge, vector addition must be performed.

Vector addition to find the resultant vector is sometimes called superposition.

Sample Problem• What is the force on the 4 C charge?

y (m)

1.0

2.0

2 C-3 C 4 C

x (m)2.01.0

Sample Problem• What is the force on the 4 C charge?

y (m)

1.0

2.0

2 C

-3 C

4 C

x (m)2.01.0

Wednesday, January 16, 2008

The Electric Field

The Electric Field

The presence of + or – charge modifies empty space. This enables the electrical force to act on charged particles without actually touching them.

We say that an “electric field” is created in the space around a charged particle or a configuration of charges.

If a charged particle is placed in an electric field created by other charges, it will experience a force as a result of the field.

Sometimes we know about the electric field without knowing much about the charge configuration that created it.

We can easily calculate the electric force from the electric field.

Why use fields?

Forces exist only when two or more particles are present.

Fields exist even if no force is present.The field of one particle only can be

calculated.

Field around + charge

The arrows in a field are not vectors, they are “lines of force”.

The lines of force indicate the direction of the force on a positive charge placed in the field.

Negative charges experience a force in the opposite direction.

Field around - charge

Field between charged plates

+ + + + + + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Field Vectors from Field Lines

The electric field at a given point is not the field line itself, but can be determined from the field line.

The electric field vectors is always tangent to the line of force at that point.

Vectors of any kind are never curvy!

Field Vectors from Field Lines

Force from Electric Field

The force on a charged particle placed in an electric field is easily calculated.

F = E q F: Force (N) E: Electric Field (N/C) q: Charge (C)

Sample Problem

The electric field in a given region is 4000 N/C pointed toward the north. What is the force exerted on a 400 μg styrafoam bead bearing 600 excess electrons when placed in the field?

Sample Problem

A 400 μg styrofoam bead has 600 excess electrons on its surface. What is the magnitude and direction of the electric field that will suspend the bead in midair?

Thursday, January 17, 2008

Superposition

Sample Problem

A proton traveling at 440 m/s in the +x direction enters an an electric field of magnitude 5400 N/C directed in the +y direction. Find the acceleration.

For Spherical Electric Fields

The Electric Field surrounding a point charge or a spherical charge can be calculated by:

E = k q / r2

E: Electric Field (N/C) k: 8.99 x 109 N m2/C2

q: Charge (C) r: distance from center of charge q (m)

Remember that k = 1/4o

Principle of Superposition

When more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges.

Again, as with force vectors, this is referred to as superposition.

Remember…

Electric field lines are NOT VECTORS, but may be used to derive the direction of electric field vectors at given points.

The resulting vector gives the direction of the electric force on a positive charge placed in the field.

Sample Problem

A particle bearing -5.0 μC is placed at -2.0 cm, and a particle bearing 5.0 μC is placed at 2.0 cm. What is the field at the origin?

Sample Problem

A particle bearing 10.0 mC is placed at the origin, and a particle bearing 5.0 mC is placed at 1.0 m. Where is the field zero?

Sample Problem

What is the charge on the bead? It’s mass is 32 mg.

E = 5000 N/C

40o

Friday, January 18, 2008

Electric Potential and Potential Energy

Electric Potential Energy

Electrical potential energy is the energy contained in a configuration of charges. Like all potential energies, when it goes up the configuration is less stable; when it goes down, the configuration is more stable.

The unit is the Joule.


Electrical potential energy increases when charges are brought into less favorable configurations

+ + - +

ΔU > 0


Electrical potential energy decreases when charges are brought into more favorable configurations.

+ - + +

ΔU < 0


+

+ ΔU = ____

-

+ ΔU = ____

Work must be done on the charge to increase the electric potential energy.

+ –

Work and Charge

For a positive test charge to be moved upward a distance d, the electric force does negative work.

The electric potential energy has increased and ΔU is positive(U2 > U1)

+

EF

+

d

Work and Charge

If a negative charge is moved upward a distance d, the electric force does positive work.

The change in the electric potential energy ΔU is negative (U2 < U1)

-

E

F

-

d

Electric Potential

Electric potential is hard to understand, but easy to measure.

We commonly call it “voltage”, and its unit is the Volt.

1 V = 1 J/C Electric potential is easily related to both

the electric potential energy, and to the electric field.

Electrical Potential and Potential Energy

The change in potential energy is directly related to the change in voltage.

U = qV U: change in electrical potential energy (J) q: charge moved (C) V: potential difference (V)

All charges will spontaneously go to lower potential energies if they are allowed to move.

Electrical Potential and Potential Energy

Since all charges try to decrease UE, and UE = qV, this means that spontaneous movement of charges result in negative U.

ΔV = ΔU / qPositive charges like to DECREASE their

potential (V < 0)Negative charges like to INCREASE their

potential. (V > 0)

Sample Problem

A 3.0 μC charge is moved through a potential difference of 640 V. What is its potential energy change?

Electrical Potential in Uniform Electric Fields

The electric potential is related in a simple way to a uniform electric field.

V = -Ed V: change in electrical potential (V) E: Constant electric field strength (N/C or V/m) d: distance moved (m)

dEV

Sample Problem

An electric field is parallel to the x-axis. What is its magnitude and direction of the electric field if the potential difference between x =1.0 m and x = 2.5 m is found to be +900 V?

Sample Problem

What is the voltmeter reading between A and B? Between A and C? Assume that the electric field has a magnitude of 400 N/C.

1.0 2.0 x(m)

y(m)

1.0

A B

C

Sample Problem

How much work would be done BY THE ELECTRIC FIELD in moving a 2 mC charge from A to C? From A to B? from B to C?. How much work would be done by an external force in each case?

1.0 2.0 x(m)

y(m)

1.0

A B

C

Tuesday, January 22, 2008

Electric Field Lines and Shielding

Monday, January 14, 2008 Charge and Polarization.

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Transcript of Monday, January 14, 2008 Charge and Polarization.