Rotating Square Loop in Constant B-field

alexcoco

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

Thanks!

Steely Dan

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.

alexcoco

Thanks, didn't think of that.