# Faraday's and Lenz's law application

1. Jan 31, 2015

### cseil

1. The problem statement, all variables and given/known data
A rectangular coil with a and b sides can rotate around the axis AA' with angular velocity ω. It is in a magnetic field as in figure.

Calculate the flux of B when the coil is orthogonal to the axis AA'. Calculate the $\epsilon_{max}$ and express the position of the coil.

2. Relevant equations
$\epsilon = -\frac{d}{dt} \phi_B$

3. The attempt at a solution

The flux when the coil is orthogonal to the axis AA' is 0.

$\phi_B = NBabcos\theta$

$\theta$ is 90°, so the flux is 0.

Now I calculate the emf.
$\epsilon = -\frac{d}{dt} \phi_B = NBab\omega sin(\omega t)$

The emf is max when $sin(\theta)$ is 1, so when $\theta$ is 90°.

Is it correct my procedure?
If yes, why emf is maximum when flux is 0?

2. Jan 31, 2015

### Staff: Mentor

Since the coil rotates about that axis, it is always orthogonal to it. I assume you mean when the plane of the coil is perpendicular to the surface of the drawing.

Yes.

What matters is not where the emf is maximum but where its rate of change is maximum.

Edit: Oops... I meant flux, not emf, of course.

Last edited: Jan 31, 2015
3. Jan 31, 2015

### cseil

Yes, sorry, I meant that.
Thank you!