Question

A plane circular coil $\text{P}$ of area $A$ is placed in a uniform magnetic induction field $B$ such that the normal to the coil plane makes an angle of ${30}^{\circ }$ with the direction of the field. The coil is now rotated in the field by ''wobbling'' such that the normal always makes angle ${30}^{\circ }$ with the field during rotation, the angular velocity of rotation being $\omega$. Then the emf induced in the coil will be :

• A. $\omega AB$
• B. $\omega BA\cos \theta$
• C. $\omega BA\sin \theta$
• D. zero

Answer 1

The correct option is D zero

Magnetic flux through the coil placed in a uniform magnetic field is given by,

$\varphi =BA\cos \theta$

Here, the magnetic field $B$, area $A$ of the coil and the angle $\theta ={30}^{\circ }$ remains constant during the rotation of the coil.

Hence, change in the magnetic flux is zero, i.e, $d\varphi =0$

So, the emf induced in the coil also be zero, i.e,

$E=|-\frac{d\varphi }{dt}|=0$

Hence, $\left(D\right)$ is the correct answer.