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