Mutual inductance problem

**rebghb** · December 18th 2010, 10:29 AM

Hello everyone!

I'm really stuck on this electromagnetics problem:
Determine the mutual inductance between an infinite wire and an equilateral triangle-shaped loop as shown in the figure.

Now, I tried putting current on the long wire so I get $\vec{B}=\frac{\mu_0 I}{2\pi r}\vec{a_{\phi}}$ or in cartesian coordinates $\vec{B}=\frac{\mu_0 I}{2\pi \sqrt{x^2+y^2}}\vec{k}$ .
Then I have to dot $\vec{B}$ with $\vec{dA}$ and integrate to find the flux, but that involves a lot of calculation and will carry an $\tan^{-1}$ somewhere, and non of the answers contain a $\tan^{-1}$ but rather a $\ln$ .
So what to do?

**malaygoel** · January 6th 2011, 05:17 AM

your expression
$\vec{B}=\frac{\mu_0 I}{2\pi \sqrt{x^2+y^2}}\vec{k}$
is wrong.
Since it is infinite in y-direction, the correct expression will be:
$\vec{B}=\frac{\mu_0 I}{2\pi x}\vec{k}$ where x-axis is from left to right

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