Given a dipole consisting of two charges +q and -q separated by a distance d, a) what is the potential at the center of the dipole? b) What is the electric field at the center of the dipole?

a) The potential can be found from the sum of the potentials for the two charges.

Does this make sense? Yes, if you take a test charge and bring it to this point, you will be gaining potential energy as you get close to +q and losing it as you get close to -q. At a point halfway between the two, these cancel.

b) The field can be found simply by adding the two fields from the point charges as was done in the last homework. Using the concepts of this chapter, we can do this by looking at the derivative of the potential, too.

You can check that this is what you would get either way.