Question

A quarter circular conducting ring of radius $r$ is rotating at angular velocity $\omega$ in uniform magnetic field as shown in figure.
EMF induced across the ring is

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

Answer 1

The correct option is B $\frac{B\omega R^2}{2}$


$d\epsilon =(\overrightarrow{v}\times \overrightarrow{B}).\overrightarrow{dl}d\epsilon =R\sin \theta \times \omega \times B\times Rd\theta \cos \theta$
$\epsilon =\int d\epsilon =B\omega R^2{\int }_0^{\frac{\pi }{2}}sin\theta cos\theta d\theta \epsilon =\frac{B\omega R^2}{2}{\int }_0^{\frac{\pi }{2}}sin2\theta d\theta \Rightarrow \epsilon =\frac{B\omega R^2}{2}$