24
CHAPTER OUTLINE
24.1
Electric Flux
24.2
Gauss’s Law
24.3
Application of Gauss’s Law
to Various Charge
Distributions
24.4
Conductors in Electrostatic
Equilibrium
24.5
Formal Derivation of
Gauss‘s Law
Gauss’s Law
ANSWERS TO QUESTIONS
Q24.1
The luminous flux on a given area is less when the sun is low in
the sky, because the angle between the rays of the sun and the
local area vector,
d
A
, is greater than zero. The cosine of this
angle is reduced. The decreased flux results, on the average, in
colder weather.
Q24.2
If the region is just a point, line, or plane, no. Consider two
protons in otherwise empty space. The electric field is zero at
the midpoint of the line joining the protons. If the fieldfree
region is threedimensional, then it can contain no charges, but
it might be surrounded by electric charge. Consider the interior
of a metal sphere carrying static charge.
Q24.3
The surface must enclose a positive total charge.
Q24.4
The net flux through any gaussian surface is zero. We can argue it two ways. Any surface contains
zero charge so Gauss’s law says the total flux is zero. The field is uniform, so the field lines entering
one side of the closed surface come out the other side and the net flux is zero.
Q24.5
Gauss’s law cannot tell the different values of the electric field at different points on the surface.
When
E
is an unknown number, then we can say
Ed
A
E
d
A
cos
cos
θθ
zz
=
. When
Ex y z
,,
bg
is an
unknown function, then there is no such simplification.
Q24.6
The electric flux through a sphere around a point charge is independent of the size of the sphere. A
sphere of larger radius has a larger area, but a smaller field at its surface, so that the product of field
strength and area is independent of radius. If the surface is not spherical, some parts are closer to the
charge than others. In this case as well, smaller projected areas go with stronger fields, so that the
net flux is unaffected.
Q24.7
Faraday’s visualization of electric field lines lends insight to this question. Consider a section of a
vertical sheet carrying charge +1 coulomb. It has
1
0
∈
field lines pointing out from it horizontally to
the right and left, all uniformly spaced. The lines have the same uniform spacing close to the sheet
and far away, showing that the field has the same value at all distances.
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Gauss’s Law
Q24.8
Consider any point, zone, or object where electric field lines begin. Surround it with a closefitting
gaussian surface. The lines will go outward through the surface to constitute positive net flux. Then
Gauss’s law asserts that positive net charge must be inside the surface: it is where the lines begin.
Similarly, any place where electric field lines end must be just inside a gaussian surface passing net
negative flux, and must be a negative charge.
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 Spring '08
 Shannon
 Charge, Electrostatics, Static Equilibrium, Electric charge, charge density, qin ρV

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