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A point charge of $-q$ is located at $z=-a$ on the $z$-axis and a point charge of $+q$ is located at $z=+a$.

1. (10 points) Write down the potential at an arbitrary point in space in spherical coordinates $(r,\theta,\phi)$.

2. (10 points) What is the leading term in the expansion of the potential for $r \gg a$, expressed in terms of the dipole moment?

(Note: Obviously, I really do want you to learn to do this one, since I did a bunch of it in lecture and asked you to finish the rest on your own. You derive a very fundamental result that will be useful to you in the years to come....so much that I'll give two hints. One is use the law of cosines to determine the distance from e.g. $+q$ to the point of observation in terms of $r$, $a$, and $\theta$ only. Second is to use the binomial expansion to extract the leading order potential term(s) for each charge and add them until you get the overall leading order term that survives - the first term or two might well cancel.)