Lecture 4 Van de Graff Generator Millikan’s Oil-Drop Experiment Electric Flux and Gauss’s Law Potential Difference Capacitance.

Lecture 4

Van de Graff Generator Millikan’s Oil-Drop Experiment Electric Flux and Gauss’s Law Potential Difference Capacitance

Experiments to Verify Properties of Charges Faraday’s Ice-Pail Experiment

Concluded a charged object suspended inside a metal container causes a rearrangement of charge on the container in such a manner that the sign of the charge on the inside surface of the container is opposite the sign of the charge on the suspended object

Millikan Oil-Drop Experiment Measured the elementary charge, e Found every charge had an integral

multiple of e Oil drop exp. q = n e

Fig. 15-21, p.515

Fig. 15-21b, p.515

Electric Flux Field lines

penetrating an area A perpendicular to the field

The product of EA is the flux, Φ

Fig. 15-25, p.517

Electric Flux, cont. ΦE = E A cos θ

The perpendicular to the area A is at an angle θ to the field

When the area is constructed such that a closed surface is formed, use the convention that flux lines passing into the interior of the volume are negative and those passing out of the interior of the volume are positive

Gauss’ Law Gauss’ Law states that the electric flux

through any closed surface is equal to the net charge Q inside the surface divided by εo

εo is the permittivity of free space and equals 8.85 x 10-12 C2/Nm2

The area in Φ is an imaginary surface, a Gaussian surface, it does not have to coincide with the surface of a physical object

insideE

o

Q

Electric Field of a Charged Thin Spherical Shell

The calculation of the field outside the shell is identical to that of a point charge

The electric field inside the shell is zero

2eo

2 r

Qk

r4

QE

Fig. 15-30, p.522

Electric Field of a Nonconducting Plane Sheet of Charge

Use a cylindrical Gaussian surface

The flux through the ends is EA, there is no field through the curved part of the surface

The total charge is Q = σA

Note, the field is uniform Gaussian surface

o2E

Electric Field of a Nonconducting Plane Sheet of Charge, cont.

The field must be perpendicular to the sheet

The field is directed either toward or away from the sheet

Parallel Plate Capacitor The device consists of

plates of positive and negative charge

The total electric field between the plates is given by

The field outside the plates is zero

o

E

Electric Potential Energy The electrostatic force is a

conservative force It is possible to define an electrical

potential energy function with this force

Work done by a conservative force is equal to the negative of the change in potential energy

Work and Potential Energy There is a uniform

field between the two plates

As the charge moves from A to B, work is done on it

W = Fd=q Ex (xf – xi) ΔPE = - W = - q Ex (xf – xi)

only for a uniform field

Fig. 16-2, p.533

Potential Difference The potential difference between points

A and B is defined as the change in the potential energy (final value minus initial value) of a charge q moved from A to B divided by the size of the charge ΔV = VB – VA = ΔPE / q

Potential difference is not the same as potential energy

Potential Difference, cont. Another way to relate the energy and

the potential difference: ΔPE = q ΔV Both electric potential energy and

potential difference are scalar quantities Units of potential difference

V = J/C A special case occurs when there is a

uniform electric field V = VB – VA= -Ex x

Gives more information about units: N/C = V/m

Energy and Charge Movements A positive charge gains electrical potential

energy when it is moved in a direction opposite the electric field

If a charge is released in the electric field, it experiences a force and accelerates, gaining kinetic energy As it gains kinetic energy, it loses an equal amount

of electrical potential energy A negative charge loses electrical potential

energy when it moves in the direction opposite the electric field

Demo

Energy and Charge Movements, cont

When the electric field is directed downward, point B is at a lower potential than point A

A positive test charge that moves from A to B loses electric potential energy

It will gain the same amount of kinetic energy as it loses in potential energy

Summary of Positive Charge Movements and Energy

When a positive charge is placed in an electric field It moves in the direction of the field It moves from a point of higher

potential to a point of lower potential Its electrical potential energy

decreases Its kinetic energy increases

Summary of Negative Charge Movements and Energy When a negative charge is placed in an

electric field It moves opposite to the direction of the

field It moves from a point of lower potential to a

point of higher potential Its electrical potential energy increases Its kinetic energy increases Work has to be done on the charge for it to

move from point A to point B

Electric Potential of a Point Charge The point of zero electric potential is

taken to be at an infinite distance from the charge

The potential created by a point charge q at any distance r from the charge is

A potential exists at some point in space whether or not there is a test charge at that point

r

qkV e