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## Homework Statement

Find the mutual inductance between an infinitely long wire and a single loop of wire separated by a distance d. (radius = a)

## Homework Equations

## The Attempt at a Solution

I've adjusted the magnetic flux density to a coordinate system to make everything easier

[tex]B =\frac{ \mu_0 I }{2\pi x}[/tex]

[tex]L_{12} = N\phi / I [/tex]

My main problem is finding the flux through the circle.

[tex]\int_{d-a}^{d+a} \int_{-\sqrt(a^2-x^2)}^{\sqrt(a^2-x^2} \frac{1}{x} dydx[/tex]

So I'm basically integrating the B field over a circle (i removed constants from the integral)

This unfortunately yields a result that isn't quite what it's supposed to be, but it seems close. Does anyone know where I went wrong?

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