(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A rectanglar loop of wire encloses an area A, has a resistance R and a self-inductance L. The loop is suspended from the mid point of one of its sides and placed in a horizontal oscillating magnetic field B = B0 sin ωt such that the field makes an angle θ with the normal to the rectangle. Show that the current in the wire is:

I = −B0 Aω(R^2 + ω^2L^2)^-0.5 cos θcos(ωt − φ)

Find the average torque acting on the rectangle from the magnetic field and

the angles θ when equilibrium is achieved.

2. Relevant equations

T⃗ =N I A⃗ ×B⃗ =M⃗ ×B⃗

3. The attempt at a solution

I've solved the first part using Ohm's Law and got the expression for the current - I now have an expression for the torque at any point which I think is correct, given by

G= -0.5 B0^2 A^2 ω sin(2θ) cos(ωt − φ) sin(ωt) (R^2 + ω^2L^2)^-0.5

but I need to average this over a cycle - rather than averaging over θ or t alone, I think I need to express θ in terms of t and then average over t, but I don't know how to do this. Any help would be much appreciated!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Average Torque on an Induced Current Loop

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