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Chapter 22
Gauss’s Law
PowerPoint® Lectures for
University Physics, Thirteenth Edition
– Hugh D. Young and Roger A. Freedman
Lectures by Wayne Anderson
Copyright © 2012 Pearson Education Inc.
Goals for Chapter 22
• To use the electric field at a surface to determine the
charge within the surface
• To learn the meaning of electric flux and how to
calculate it
• To learn the relationship between the electric flux
through a surface and the charge within the surface
• To use Gauss’s law to calculate electric fields
• To learn where the charge on a conductor is located
Copyright © 2012 Pearson Education Inc.
Introduction
• Would the girl’s hair
stand on end if she were
inside the metal sphere?
• Symmetry properties
play an important role in
physics.
• Gauss’s law will allow
us to do electric-field
calculations using
symmetry principles.
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Charge and electric flux
• Positive charge within the box produces outward
electric flux through the surface of the box, and
negative charge produces inward flux. (See Figure
22.2 below.)
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Figure 22.3 Zero net charge inside a box
• There are three ways in which there is zero net
charge inside a box and no net electric flux
through the surface of the box.
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What affects the flux through a box?
• As Figure 22.4 below shows, doubling the charge
within the box doubles the flux, but doubling the size
of the box does not change the flux. Why?
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Calculating electric flux
• The electric flux depends on the intensity of the
electric field E and the orientation of the surface with
respect to the electric field.
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Example 22.1 Electric flux through a disk
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Example 22.2 Electric flux through a cube
An imaginary cube of side
L is in a region of uniform
electric field E. Find the
electric flux through each
surface of the cube when
(a) it is oriented with two
of its faces perpendicular
to E.
Insanity is doing the same thing
over and over and expecting a
different result.
Albert Einstein
Copyright © 2012 Pearson Education Inc.
Gauss’s Law
• Gauss’s law is an alternative to Coulomb’s law and is completely
equivalent to it.
• What did you find out about Gauss?
1.
2.
3.
4.
5.
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Figure 22.11 Point charge centered in a spherical surface
• The flux through the sphere
is independent of the size of
the sphere and depends
only on the charge inside.
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Point charge inside a nonspherical surface
• As before, the flux is independent of the surface and depends only
on the charge inside. (See Figure 22.12 below.)
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Example 22.3 Electric flux through a sphere
A point charge q=+3.0 µC is
surrounded by an imaginary
sphere of radius = 0.20 m
centered on the charge. Find
the resulting electric flux
through the sphere.
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Positive and negative flux
• Flux is positive (outward) if the enclosed charge is
positive, and negative (inward) if the charge is
negative.
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Example 22.4 Electric flux and enclosed charge
• What is the electric flux through each of the following
surfaces: A, B, C and D.
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Gaussian Surfaces
Gaussian surfaces are imaginary. We use them
as a convenience, to ease the calculation of
electric flux, electric field, area or enclosed
charge.
What Gaussian surface did you bring with you
tonight?
While any closed surface could be a Gaussian
surface, we typically use just a few specific
types. What are they? Why are they so useful?
Copyright © 2012 Pearson Education Inc.
Applications of Gauss’s law
• Under electrostatic conditions, any excess charge on a conductor
resides entirely on its surface. Our EE’s have a name for this,
what is it?
• Example 22.5 uses Figure 22.18 below right.
This answers the question on slide 3
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Example 22.6 Field of a line charge
Electric charge is distributed
uniformly along an infinitely
long, thin wire. The charge per
unit length is λ (assumed
positive). Find the electric field
using Gauss’s Law.
Looking from the end of the wire.
The electric field radiates out
radially from the wire. Therefore
only the circumference of the
cylinder contributes to the electric
flux.
Copyright © 2012 Pearson Education Inc.
Notice that E is inverse r, not r2, in this case.
Example 22.7 Field of an infinite sheet of charge
Use Gauss’s Law to find
the electric field caused by
a thin, flat, infinite sheet
with a uniform positive
surface charge density σ.
In this case, the electric flux emerges
only from the ends.
Could we have used a different
Gaussian surface to solve this
problem? If so, which one?
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Example 22.8 Field between two parallel conducting
plates
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Example 22.9 A uniformly charged sphere
We already know the electric field outside the sphere. What is the
electric field inside a uniformly charged sphere?
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Charges on conductors
• In the text, follow the discussion on charges in a conductor having a
cavity within it. Figure 22.23 below will help the explanation.
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A conductor with a cavity
• Follow Conceptual Example 22.11 using Figure 22.24 below.
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Testing Gauss’s law experimentally
• Follow the discussion of Faraday’s icepail experiment, which
confirmed the validity of Gauss’s law. Use Figure 22.25 below.
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The Van de Graaff generator
• The Van de Graaff generator, shown in Figure 22.26 below,
operates on the same principle as in Faraday’s icepail experiment.
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Electrostatic shielding
• A conducting box (a Faraday cage) in an electric field
shields the interior from the field. (See Figure 22.27
below.)
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Field at the surface of a conductor
• The electric field at the
surface of any conductor is
always perpendicular to the
surface and has magnitude
 / 0 .
• Follow the discussion in the
text, using Figure 22.28 at
the right.
• Follow Conceptual Example
22.12.
• Follow Example 22.13,
which deals with the electric
field of the earth.
Copyright © 2012 Pearson Education Inc.
Goals for Chapter 22
• To use the electric field at a surface to determine the
charge within the surface
• To learn the meaning of electric flux and how to
calculate it
• To learn the relationship between the electric flux
through a surface and the charge within the surface
• To use Gauss’s law to calculate electric fields
• To learn where the charge on a conductor is located
Copyright © 2012 Pearson Education Inc.