March 5th, 1998

PHYSICS 742 - Midterm

1) Two infinite, grounded, conducting planes are located at x=d/2 and x=-d/2. A point charge is placed between the planes at a point $P \equiv (x',y',z')$.

(a) Find the location and value of all the image charges needed to satisfy the boundary conditions.

(b) Write down the Green's function G(x,x').

(10 points)

2) Three charges are arranged in a linear array. The charges have values: -2q, +q, +q and they are located at $O \equiv (0,0,0)$ $P_1 \equiv (0,0,a)$, $P_2 \equiv (0,0,-a)$, respectively.

(a) Find the potential and write an expansion for it that is valid at large distances from the array ($\mid {\bf r} \mid \gt\gt a$).

(10 points)

(b) Find the non vanishing terms of the quadrupole moment tensor for this charge distribution.

(5 points)

3) Find the electrostatic energy of two concentric spherical shells of radii a and b (b>a) and uniformly distibuted charges q_a and q_b, respectively.

(5 points)