PY212 SPRING 2001 EXAM 1 SOLUTIONS

P1A: 12 pF. First do 120, 60, 40 pF in series. Then that result
(20 pF) in parallel with 10 pF. Then that result (30 pF) in series with 20.

P1B: F F F T F T T. Read the book!

P1C: 3.125E15 electrons. W=0 (closed path). around 1000 N. 9.4e6 Nm^2/C.
We took off 1 out of 3 points if you didn't calculate a numerical answer
(c)... you were supposed to estimate "r". Most people realized this.
For (d), the point is the flux through 1 face is 1/6 the total flux = Qenc/e0.

P2: Superposition!
    (a) arrows go from + to -. More arrows coming from +2q than going
        into -q. Strictly speaking there should be 2x as many arrows.
    (b) -7kq^2/4a^2 (i-hat)
    (c) -7kq^2/2a (the sum of three terms)
    (d) the sum of three terms:
        -kq/sqrt((x+a)^2 + y^2) + k2q/sqrt(x^2 + y^2) -kq/sqrt((x-a)^2 + y^2)

P3: Use Gauss' Law.
    r < a, E = rho r / 3 e0
    a < r < b, E = 0 (inside conductor)
    r > B, E = rho A^3 / 3 e0 r^2
 
P4: (a) 15.93 pF
    (b) 2.87 microJ
    (c) 1.33 cm (use KE + PE method)