24
Gauss’s Law
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
ANSWERS TO QUESTIONS
Q24.1
The luminous ﬂ
ux 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
r
A
, is greater than zero.
The cosine of this angle is reduced. The decreased ﬂ
ux
results, on the average, in colder weather.
Q24.2
The surface must enclose a positive total charge.
Q24.3
The net ﬂ
ux through any gaussian surface is zero. We
can argue it two ways. Any surface contains zero charge,
so Gauss’s law says the total ﬂ
ux is zero. The F
eld is
uniform, so the F
eld lines entering one side of the closed
surface come out the other side and the net ﬂ
ux is zero.
*Q24.4
(i) Equal amounts of ﬂ
ux pass through each of the six faces of the cube.
Answer (e).
(ii) Move the charge to very close below the center of one face, through which the ﬂ
ux is then
q
/2
∈
0
.
Answer (c).
(iii) Move the charge onto one of the cube faces. Then the F
eld has no component perpendicular
to this face and the ﬂ
ux is zero.
Answer (a).
*Q24.5
(i) Answer (a).
(ii) the ﬂ
ux is zero through the two faces pierced by the F
lament.
Answer (b).
*Q24.6
(i) Answer (a).
(ii) The ﬂ
ux is nonzero through the top and bottom faces, and zero through the other four faces.
Answer (c).
*Q24.7
(i) Both spheres create equal F
elds at exterior points, like particles at the centers of the spheres.
Answer (c).
(ii) The F
eld within the conductor is zero. The F
eld within the insulator is 4/5 of its surface
value.
Answer (f).
Q24.8
Gauss’s law cannot tell the different values of the electric F
eld at different points on the surface.
When
E
is an unknown number, then we can say
Ed
A
E
d
A
cos
cos
θθ
∫∫
=
. When
Exyz
,,
( )
is an unknown function, then there is no such simpliF
cation.
Q24.9
The electric ﬂ
ux 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 F
eld at its surface, so that the product
of F
eld 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
F
elds, so that the net ﬂ
ux is unaffected.
27
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Chapter 24
Q24.10
Inject some charge at arbitrary places within a conducting object. Every bit of the charge repels
every other bit, so each bit runs away as far as it can, stopping only when it reaches the outer
surface of the conductor.
*Q24.11
(a)
Let
q
represent the charge of the insulating sphere. The F
eld at A is (4/5)
3
q
/[4
p
(4 cm)
2
∈
0
].
The F
eld at B is
q
/[4
p
(8 cm)
2
∈
0
]. The F
eld at C is zero. The F
eld at D is
q
/[4
p
(16 cm)
2
∈
0
].
The ranking is A
>
B
>
D
>
C.
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 Spring '11
 williams,frank
 Electron, Charge, Static Equilibrium, Electric charge, Fundamental physics concepts, charge density, Qin

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