# Math Help - Mutual inductance problem

1. ## Mutual inductance problem

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?

$\vec{B}=\frac{\mu_0 I}{2\pi \sqrt{x^2+y^2}}\vec{k}$
$\vec{B}=\frac{\mu_0 I}{2\pi x}\vec{k}$ where x-axis is from left to right