Emf in coil rotating inside magnetic field

[songoku]

Homework Statement

Please see below

Relevant Equations

emf = - dφ / dt

My answer is (B) but the answer key is (A).

My working:
$$\varepsilon=-\frac{d\phi}{dt}$$
$$=-AB\frac{cos\omega t}{dt}$$
$$=AB\omega \sin \omega t$$

Why the answer is zero? I thought the flux will be zero, not the emf.

Thanks

 

[renormalize]

Why the answer is zero? I thought the flux will be zero, not the emf.

How much of the magnetic field $B$ is normal to the area $A$?

 

[kuruman]

Look at the deifiniton for flux. $\Phi=(\mathbf B\cdot\mathbf{\hat n})~A$ where $\mathbf {\hat n}$ is perpendicular to the plane of the coil. As you say, the flux is zero. You get an induced emf if the flux changes with time. Does it?

 

[songoku]

How much of the magnetic field $B$ is normal to the area $A$?

Look at the deifiniton for flux. $\Phi=(\mathbf B\cdot\mathbf{\hat n})~A$ where $\mathbf {\hat n}$ is perpendicular to the plane of the coil. As you say, the flux is zero. You get an induced emf if the flux changes with time. Does it?

Ah I see. Seeing the rotation of the coil with respect to magnetic field, there won't be any B passing through the coil so the rate of change of magnetic flux is zero.

Thank you very much renormalize and kuruman