Question

An $\text{S}$ shaped conducting wire consists of two semicircles, each of radius $r=5\text{cm}.$ The wire is rotating about point $O$, in a uniform magnetic field of magnitude $1.5\text{T}$ perpendicular to the plane of wire with an angular velocity of $8\text{rad/s}$ as shown in the figure. Calculate the emf developed across the ends of the wire.

Answer 1

The effective length of the wire is,

$l=2r+2r=4r=4\times 0.05=0.2\text{m}$

Now, emf developed across its ends is,

$E=\frac{B\omega l^2}{2}$

$=\frac{1.5\times 8\times {0.2}^2}{2}=0.24\text{V}$

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