Question

A rectangular coil of wire is placed in a uniform magnetic field such that the plane of the coil is parallel to the magnetic field. The magnetic flux linked with the coil and the emf induced are respectively:

• A. Zero and zero
• B. Zero and maximum
• C. Maximum and zero
• D. Maximum and maximum

Answer 1

Answer: (B)

Zero and maximum

Since the plane of the coil is parallel to the magnetic field, the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are perpendicular to each other.

Hence, the magnetic flux $=\overrightarrow{B}.\overrightarrow{A}=0$

The emf induced in the coil $=\frac{d\varphi }{dt}$ $=\frac{d\left(BAcos\omega t\right)}{dt}$ $=BA\omega sin\omega t$ $=BA\omega sin\theta$ which is maximum for $\theta ={90}^{\circ }$