Physics 7B: Saturday Midterm 2 Review Problems
Natania Antler
(Dated: March 30, 2010)
The review session will be held on Saturday, April 3rd from 24 PM in 155 Dwinelle. Try these
problems before coming to the session. I will work through these problems on the board, and answer
questions. The solutions will be posted Saturday afternoon. Good luck studying!
1.
CHARGED SLABS
ρ
+ ρ

ρ
2d
d
d
z
Z = 0
FIG. 1: Charged slabs for parts (a) and (b).
Consider charged slabs as shown in Figure
1
.
(a) Consider an infinite plane slab in the xy plane of thickness 2d, which has a uniform charge density
ρ
. Find the E
field everywhere as a function of z (the slab is centered about z = 0).
(b) Now find the E field everywhere for two slabs stacked on top of each other, each with thickness d. The top slab
has charge density

ρ
and bottom has charge density +
ρ
. The plane where the slabs meet is at z = 0.
(c) Can you justify why you used the Gaussian surface(s) that you did for (a) and (b)?
2.
HOLE IN A PLANE
Imagine a uniformly positively charged plate in the xy plane with a hole cut into it. The hole has diameter w, and
the plane has surface charge
σ
.
(a) What is the electric field as a function of z directly above the hole? Assume
z
w
.
(b) What is the potential as a function of z?
Again, assume
z
w
.
(Hint 1: You will need to be careful about
choosing your reference point. Hint 2: Check your answer by taking the gradient, recalling that in this case
E
=

∂V
∂z
)
(c) Let
z
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 Spring '08
 ZETTLE
 Charge, Electric charge, Dwinelle

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