Physics 200B Mid Term Exam 11-Feb-04

Dr. Cebra Name: _________________

Instructions: Work all parts of both problems (each problem worth 50 points). No notes, calculators, etc. Please write your name on every page.

1. A grounded conductor consists of the z = 0 plane together with a hemispherical boss of radius a. A point charge, q, is located directly above the boss at r = b and q = 0.

a) Using the methods of images, find an expression for the potential F(r,q) in the region above the conductor. Verify that the potential vanishes on the surface. (Hint: use three images charges)

b) Find the induced surface charge density, s(q) on the boss and calculate the total charge on the boss. What is the total charge on the plane excluding the boss?

c) Find the force on the boss.

Phys 200B Name: _________________

2. A hollow, non-conducting cylinder with radius r = a has a surface charge density given by s(q) = s₀cos(f), where s₀ is a constant.

a) Assuming the cylinder is infinite in the z direction, determine F(r,f) for all space. Demonstrate that your solution matches all the boundary conditions.

b) Accurately sketch the resultant field lines.

c) Now consider a finite cylinder of length L for which the two circular end caps are both held at ground potential. Qualitatively describe how your solution to F(r,f,z) will change and make a sketch of the resultant field lines.