Question

A semicircular loop of radius R is rotated with an angular velocity $\omega$. perpendicular to the plane of a uniform magnetic field B as shown in the figure. Emf induced in the loop is :

• A. $B\omega R^2$
• B. $\frac{1}{2} B\omega R^2$
• C. $\frac{3}{2} B\omega R^2$
• D. $\frac{1}{4} B\omega R^2$

Answer 1

Answer: (B)

(2)

Answer 2

The problem describes a semicircular loop of radius R rotating with an angular velocity $\omega$ about its diameter in a uniform magnetic field B.

The induced EMF in a rotating conductor of length L about one end is given by:

$\mathcal{E} = \frac{1}{2} B \omega L^2$

In this case, the effective length is the radius R. The EMF induced in the semicircular loop is equivalent to the EMF induced in a straight rod of length R rotating about one end (the center of the diameter) in the magnetic field B.

Therefore, the induced EMF is:

$\mathcal{E} = \frac{1}{2} B \omega R^2$