Assignment 1

Due: Friday, 10 October 2003

1. Problem 2.1

2. Problem 2.41

3. An electric field has the form,

E = C_or^-3(2 cos[theta],sin[theta])

in polar coordinates. Here, C_o is a constant, r is the radial coordinate and theta is the polar angle. Find and sketch the field lines.

4. A particle of mass m and charge -q_o (q_o>0) is held at height h above the center of a uniformly charged ring (radius R and charge Q>0). If mass m is released and forced to move along the axis of the ring, solve for and describe its subsequent motion. Consider the case, h << R. Roughly, what constraint must be placed on h to ensure that your solution is valid?

5. Find the electric field for a charged sphere of radius R with a spherically symmetric charge distribution (the charge distribution depends only on the radius r). Find the force between two charged spheres; both spheres have uniform charge distributions. The spheres have radius R₁ and R₂, total charges Q₁ and Q₂, and are separated by distance D > R₁+R₂.