Why Does Reversing Current Source in EMF Problems Work?

[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.

Homework Statement

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

Homework Equations

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

 

[Troels]

Is it something to do with mutual inductance?

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.