Question

Th circular arc (in $x-y$plane) shown in figure rotates (about $z-axis$) with a constant angular velocity $\omega$. Time in a cycle for which there will be induced $emf$ in the loop is:

• A. $\frac{\pi }{2\omega }$
• B. $\frac{\pi }{\omega }$
• C. $\frac{2\pi }{3\omega }$
• D. $\frac{3\pi }{2\omega }$

Answer 1

The correct option is A $\frac{\pi }{2\omega }$

Angular velocity=$\omega$

$B.A=\varphi ,B.A=BA$

$emf=\frac{d\theta }{dt}$

$=BA$

$=A\frac{dA}{dt}$

Let $r$ be the radius.

$dA=\frac{r^2}{2}d\theta$

$dE=B.\frac{r^2}{2}\frac{d\theta }{dt}$

$\frac{B{r}^2\omega }{2}$

Time it will be therefore when there is charge in ares.

$t=\frac{\pi }{2\omega }$