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A wheel consiting of a large number of thin conducting spokes is free to rotate about its axle. The brush makes contact one spoke at a time. There is a uniform B field pointing into the page. The wheel is initially at rest.

R = radius of wheel

J = moment of inertia of wheel

L = inductance of circuit

V = voltage

QUESTION:

Find an expression relating ω(t) with I(t) by calculating the torque on the wheel.

ATTEMPT:

I tried using τ = dL/dt and L=Jω to get that τ = J*dω/dt. For the other half of the expression I use τ = r x F. I am unclear how to do that part. Any help would be awesome, thanks!