It's electromagnetics time again.(adsbygoogle = window.adsbygoogle || []).push({});

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 distancedfrom the center of a conducting circular loop of radiusb. Find the mutual inductance between them.

I know, by Ampere's law, the the magnetic flux density of the wire will be

[tex]\vec{B}=\frac{\mu_{0}I}{2 \pi r}\hat{a}_{\phi}[/tex]

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:

[tex]\phi = \int_{S}\vec{B} \cdot d \vec{s}[/tex]

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Mutual Inductance and Ampere's law

**Physics Forums | Science Articles, Homework Help, Discussion**