Mutual inductance of a coil and straight wire

[Trogdor27]

Homework Statement

A single rectangular loop is placed distance C from a wire of current I. The dimensions of the loop are BxA.

The loop and wire both lie in the same plane, and a is at right angles to I.

Derive an expression for the mutual inductance, given that you found flux in a previous question.

Homework Equations

B = mu I / 2R

Mutual inductance = flux(1)/i(2) = flux(2)/i(1)

The Attempt at a Solution

I have found the flux through the coil (I think it is right?):

flux = int(B.dA)

take the area as AxB, and let dA = b dr. The limits on the integral become c and c+a.

Integrate to find magnetic flux.

After finding flux, I am not sure how to go from here to the mutual inductance. I could just divide by i, but this seems WAY too simple for a question worth a lot of marks.

Or is it really just that simple?

 

[Redbelly98]

Welcome to Physics Forums.

Homework Statement

A single rectangular loop is placed distance C from a wire of current I. The dimensions of the loop are BxA.

The loop and wire both lie in the same plane, and a is at right angles to I.

Derive an expression for the mutual inductance, given that you found flux in a previous question.

Homework Equations

B = mu I / 2R

Mutual inductance = flux(1)/i(2) = flux(2)/i(1)

The Attempt at a Solution

I have found the flux through the coil (I think it is right?):

flux = int(B.dA)

take the area as AxB, and let dA = b dr. The limits on the integral become c and c+a.

Integrate to find magnetic flux.

After finding flux, I am not sure how to go from here to the mutual inductance. I could just divide by i, but this seems WAY too simple for a question worth a lot of marks.

Or is it really just that simple?

Yes, that looks right.

By the way, don't forget the "π" in

B = μ_o I / (2π r)