1. Find the series expansion for tan (x) for small x. Then, take the derivative of that series, and compare it to the series expansion of what you know to be the derivative of tan (x).

2. A tiny ball of mass m and charge q is constrained to travel along the x-axis. It begins quite near the origin. There are, glued down at x=-L and x=+L, two identical point charges Q. All charges here are positive. Show that the point charge oscillates, and determine the frequency of its oscillations. (At least, figure out the force on q when its x-value is small.)

3. It's easy to see that, at points along the z axis, an electric potential kQ/sqrt(R^2 +z^2) results from a uniformly charged ring of radius R, with a total charge of Q, lying in the xy plane and centered at the origin. (k=1 over 4 pi epsilon-nought) Show that for z>>R, this reduces to the electric potential due to a point charge Q, as you would expect. What is the first-order correction to the point charge potential?

4. The charge on a capacitor often depends on time according to the following expression: q(t)=Q(1-exp(-t/RC)). Suppose that after 1 picosecond, there's 1 nanocoulomb of charge on this capacitor. How much charge is on the capacitor after 2 picoseconds?