Obtain the electric field at point (0, 0, z) for a line of length 2L along the x axis. The line is
centered about the origin and carries a uniform line charge density ρl
.
Problem 2: Obtain the electric field at point (0, 0, z) for a circular loop of radius a lying on the plane
z = 0, which carries a nonuniform line charge density ρl(φ) = ρ0 cos φ.
Problem 3: Obtain the electric field at point (0, 0, z) for a finite plane {x ∈ [−a, a], y ∈ [−b, b], z = 0} that
carries a uniform surface charge density ρs. Hint:
Z
dx
(x
2 + y
2 + z
2)

3/2

x
(y
2 + z
2)
p
x
2 + y
2 + z
2
and
Z
dy
(y
2 + z
2)
p
a
2 + y
2 + z

2

1
az
tan−1 ay
z
p
a
2 + y
2 + z
2
. Note that, if you take the limit as a and b go to
infinity in the final expression, you must get E =
ρs
2ε0
aˆz.
Problem 4: Two spheres with radii a and b (b > a) are concentric. A volume charge density ρv(r) is
distributed in the region a < r < b, and is given by ρv(r) = ρ0 1 r 2 , where ρ0 is a constant. On the surface r = b, there exists a uniform surface charge density ρs. Find the electric field using Gauss’s law in: (a) r < a, (b) a < r < b, and (c) r > b.
1
Problem 5: An infinite cylinder along the z axis with radius a is coaxial with an infinite line, located at
the origin, carrying a uniform line charge density ρl
. On the surface ρ = a, there exists a uniform surface
charge density ρs. Find the electric field using Gauss’s law in: (a) ρ < a, and (b) ρ > a.

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