Magnetic field question

1. Feb 23, 2008

joker_900

First up, I have got the answer required - however I don't know why this has produced the right answer. I thought it might and tried it, but I don't know why it worked! I would appreciate some insight.

1. The problem statement, all variables and given/known data
A small coil of N turns and area A carrying a constant current I and a circular ring with radius R have a common axis. The small coil moves along the axis so that it's distance from the centre of the ring is given by d = d0 + acoswt. Show that the EMF induced in the ring is

(3/2) mu NAIw aR^2 d (R^2 + d^2)^(-5/2) sinwt

2. Relevant equations

3. The attempt at a solution

OK so for some reason, it worked when I switched the problem around - I said the current is in the ring, not the coil. Then from a previous problem I knew the magnetic field due to current in the ring at any point on its axis is in the direction of the axis and magnitude

0.5 mu IR^2 (R^2 + x^2)^(3/2)

As the coil is small, the field can be considered constant across it's cross-section, and along it's length, so each turn has the same uniform field through it and the total flux linkage is

0.5 Nmu IR^2 (R^2 + d^2)^(3/2)

Then I differentiated to get the EMF and the answer comes out.

But why am I allowed to pretend the current is in the ring instead of the coil? Is it something to do with mutual inductance?

Thanks

2. Feb 23, 2008

Troels

Spot on! This is one of those problems where a direct solution would be miserable, but become very simple when invoking the argument of mutual inductance.