We worked out the multiple expansion for the vector potential of a line current because that's the most common type, and in some respects the easiest to handle. For a volume current J: a) Write down the multipole expansion, analogous to the equation µol A(r) = 4л 1 dľ = 1 for. ' Pn (cos 0') dľ', L pn+1 47 n=0 b) Write down the multipole expansion, and prove that it vanishes. c) Using the equation a = r x dl, and m = I i da = la. Show that the dipole moment can be written as m = (r x J) dt.

We worked out the multiple expansion for the vector potential of a line current because that's the most common type, and in some respects the easiest to handle. For a volume current J: a) Write down the multipole expansion, analogous to the equation µol A(r) = 4л 1 dľ = 1 for. ' Pn (cos 0') dľ', L pn+1 47 n=0 b) Write down the multipole expansion, and prove that it vanishes. c) Using the equation a = r x dl, and m = I i da = la. Show that the dipole moment can be written as m = (r x J) dt.