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MT2_review - Physics 7B Saturday Midterm 2 Review Problems...

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Physics 7B: Saturday Midterm 2 Review Problems Natania Antler (Dated: March 30, 2010) The review session will be held on Saturday, April 3rd from 2-4 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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