Question

A rectangular coil $ABCD$ is rotated anticlockwise with a uniform angular velocity about the axis shown in figure. The axis of rotation of the coil as well as the magnetic field $B$ is horizontal. The induced emf in the coil would be minimum when the plane of the coil

• A. is horizontal
• B. makes and angle ${45}^o$ with direction of magnetic field
• C. is at right angle to the magnetic field
• D. makes and angle of ${30}^o$ with the magnetic field
• E. answer required

Answer 1

Answer: (C)

is at right angle to the magnetic field

Let the angle between magnetic field and the line perpendicular to the surface of rectangular coil be $\theta$.

Hence the flux through the coil is $\varphi =\overrightarrow{B}.\overrightarrow{A}=BAcos\theta$

Hence the induced emf=Rate of change of flux=$-\frac{d\varphi }{dt}=BAsin\theta \frac{d\theta }{dt}=BA\omega sin\theta$

Hence it is minimum when $\theta =0^{\circ },{180}^{\circ }$

Which means when the plane of coil is at right angle to the magnetic field.