To check your understanding of this chapter, you should complete at least the first two cases from the following activity. (The mathematical manipulations in all of the cases are essentially the same, although different cases will teach you different things about the physics.) A discussion of some of the most important observations you may make while completing this activity is contained in the following section. Also included in the next section are the final answers to all of the problems in this activity, so you can compare and contrast the different cases.

1. Two charges $+Q$ and $+Q$ are placed on a line at $z=D$ and $z=-D$ respectively. What is a fourth order approximation to the electrostatic potential $V(0,0,z)$ for $|z| \ll D$? For what values of $z$ does your series converge? For what values of $z$ is your approximation a good one? Which direction would a test charge move under the influence of this electrostatic potential?
2. As above, but for $|z| \gg D$.
3. As above, but for $V(x,0,0)$ and $|x| \ll D$.
4. As above, but for $|x| \gg D$.
5. Repeat all four cases above with two charges $+Q$ and $-Q$ placed on a line at $z=+D$ and $z=-D$ respectively.