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Rotating Square Loop in Constant B-field

by alexcoco
Tags: flux, magnetism
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Apr21-12, 08:43 PM
P: 2
1. The problem statement, all variables and given/known data
A square loop (length along one side = 20 cm) rotates in a constant magnetic field which has a magnitude of 2.0 T. At an instant when the angle between the field and the normal to the plane of the loop is equal to 20 and increasing at the rate of 10/s, what is the magnitude of the induced emf in the loop?

a. 13mV
b. 0.27V
c. 4.8mV
d. 14mV
e. 2.2mV
2. Relevant equations

[itex]\epsilon[/itex] = - [itex]\frac{d\Phi}{dt}[/itex]

[itex]\Phi[/itex] = BAcos([itex]\theta[/itex]) = BAcos([itex]\omega[/itex]t)

[itex]d\Phi[/itex] = -BA[itex]\omega[/itex]sin([itex]\omega[/itex]t)

3. The attempt at a solution

I'm trying to study for an exam and I've got this practice question that I can answer but my answer never matches. I keep getting b as an answer and I'm not sure if it's right.

[itex]\epsilon[/itex] = BAcos([itex]\omega[/itex]t) = (2T)(0.2m)2(10)sin(10t)

I use t = 2s since it asks for [itex]\theta[/itex] = 20 and I get

[itex]\epsilon[/itex] = (2T)(0.2m)2(10)sin(20) ≈ 0.27 V

Am I making a mistake or a wrong assumption anywhere or could it be the answer is incorrectly marked?

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Steely Dan
Apr21-12, 09:30 PM
P: 317
Using "10" might be fine inside the argument of the sine function, but if you're taking it outside when you take the derivative, you need to convert it to rad/s.
Apr21-12, 09:51 PM
P: 2
Thanks, didn't think of that.

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