# Magnetic Vector Potential

1. Dec 8, 2008

### lovinuz

1. The problem statement, all variables and given/known data
A finite wire lies on the z axis and extends from the point z=-V to z=+V. the equation from griffiths introduction to electrodynamics (equation 5.62) can be used to determine the vector potential at a point in the xy plane a distance s from the wire to be A=mu(naught)I/4pi [integral of dx'/sqrt(s square + x' square) from -V to +V] k, where k is the direction vector. after calculation, it gives: A=mu(naught)I/2pi ln(V/s + sqrt[1+(V/s)square] k. for a finite wire, we should take the limit as V goes to infinity, but the result blows up in this case. the first part of my question is to show that in the limit V goes to infinity, the above result becomes A=mu(naught)I/2pi ln(2V/s) k this is simple as we can take V/s common in the logarithm part, and then take the limit of V to infinity to get the required equation. the second part of the question asks to take the curl of the achieved equation using cylindrical coordinates, and thereby determining the magnetic field B at points in the xy plane. this is where i get stuck!
the third part is even harder and gives us that an equally good vector potential is given by A'=A+(delta)(lambda), where lambda is any scalar field we might wish to choose. what i need is a suitable choice for lambda so that A' remains finite in the limite V goes to infinity.

these two parts are giving me a hard time, i am sorry if i was very untidy in my representation, but if anyone could help me it wud be really nice, thanks!