Download Lecture 4

Lecture 4
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Van de Graff Generator
Millikan’s Oil-Drop Experiment
Electric Flux and Gauss’s Law
Potential Difference
Capacitance
Experiments to Verify
Properties of Charges
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Faraday’s Ice-Pail Experiment
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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
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Measured the elementary charge, e
Found every charge had an integral
multiple of e
Oil drop exp.
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q=ne
Fig. 15-21, p.515
Fig. 15-21b, p.515
Electric Flux
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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.
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ΦE = E A cos θ
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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
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Gauss’ Law states that the electric flux
through any closed surface is equal to the
net charge Q inside the surface divided by
εo
E 
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Qinside
o
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
Electric Field of a Charged
Thin Spherical Shell
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The calculation of the field outside the shell is
identical to that of a point charge
Q
Q
E
 ke 2
2
4r  o
r
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The electric field inside the shell is zero
Fig. 15-30, p.522
Electric Field of a Nonconducting
Plane Sheet of Charge
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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

E
2 o
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Note, the field is
uniform Gaussian surface
Electric Field of a Nonconducting
Plane Sheet of Charge, cont.
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The field must be
perpendicular to
the sheet
The field is
directed either
toward or away
from the sheet
Parallel Plate Capacitor
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The device consists of
plates of positive and
negative charge
The total electric field
between the plates is
given by

E 
o
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The field outside the
plates is zero
Electric Potential Energy
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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
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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)
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only for a uniform
field
Fig. 16-2, p.533
Potential Difference
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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
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ΔV = VB – VA = ΔPE / q
Potential difference is not the same as
potential energy
Potential Difference, cont.
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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
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V = J/C
A special case occurs when there is a
uniform electric field
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DV = VB – VA= -Ex Dx
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Gives more information about units: N/C = V/m
Energy and Charge
Movements
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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
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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
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Energy and Charge
Movements, cont
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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
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When a positive charge is placed in
an electric field
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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
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When a negative charge is placed in an
electric field
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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
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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
q
V  ke
r
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A potential exists at some point in
space whether or not there is a test
charge at that point