# Mutual Inductance and Ampere's law

1. Dec 6, 2005

### Antepolleo

It's electromagnetics time again.
I'm horribly stuck on a homework problem. It has to do with mutual inductance, and I know how the problem works conceptually, but I'm having a difficult time with the mathematics. The problem:

A very long (read: infinite) wire is a distance d from the center of a conducting circular loop of radius b. Find the mutual inductance between them.

I know, by Ampere's law, the the magnetic flux density of the wire will be
$$\vec{B}=\frac{\mu_{0}I}{2 \pi r}\hat{a}_{\phi}$$

With r being the distance from the wire. I know this will cause a magnetic flux to pass through the surface enclosed by the circular loop, and it will not be uniform. I can't for the life of me figure out how to put this in mathematical terms. I'm pretty sure I need to use this:

$$\phi = \int_{S}\vec{B} \cdot d \vec{s}$$

But I'm not sure where to put the differential, or even which coordinate system to use.

Last edited: Dec 6, 2005
2. Dec 7, 2005

### emptymaximum

how is the loop oriented in relation to the wire?