Question

charges Q+ and -2Q exist along the z-axis (x,y=0 for each) separated by distance of 'D'.

a) calculate the total charge Q TOT and dipole moment

b) Assuming the z - axis points up, w rite the potential ? ( ? , ? ) for distances far away using the multipole expansion keeping the first TWO non - zero terms. This should be very quick , you don’t need to rederive anything.

c) For a point on the z - axis at a distance z=10d from the center of these two charges, how much larger is the monopole term than the dipole term? How about at z=100d?

d ) Show that if you choose a different origin, you get a different answer for the dipole moment in this case (that is only true if Q TOT is nonzero!). Is it reasonable that you get a different answer? - comment briefly.

Answer 1