# Moving magnetic dipole into current loop

1. Nov 3, 2014

### azupol

1. The problem statement, all variables and given/known data
A magnetic dipole m is moved from infinitely far away to a point on the axis of a fixed, perfectly conducting (zero resistance) circular loop of radius a and self-inductance L. In its final position the dipole is oriented along the axis of the loop and is a distance z from its centre. If the current in the loop is initially zero (i.e. when the dipole is infinitely far away):
a) Find the current in the loop when the dipole is in its final position
b) Calculate the force between the loop and the dipole (in its final position).

2. Relevant equations
Vector potential of the dipole
Magnetic flux is LI, L is the self-inductance and I is the current

3. The attempt at a solution
I'm not sure how to start this problem. Conceptually, I think that moving in the dipole from infinity will induce a current in the loop due to the changing magnetic field, but I can't come up with a rigorous argument.

2. Nov 9, 2014