Question

A square loop of side $a$ is rotating about its diagonal with angular velocity $\omega $ in a perpendicular magnetic field $\overset{ \rightarrow }{B}$ . It has $10$ turns. The emf induced is

• A. $Ba^{2}sin \omega t$
• B. $Ba^{2}cos \omega t$
• C. $5\sqrt{2}Ba^{2}$
• D. $10Ba^{2}\omega sin \omega t$

Answer 1

Answer: (D)

Magnetic flux linked with loop at any instant,
$\phi=BAcos \theta $
$\phi=Ba^{2}cos \omega t$
Emf induced
$\therefore \epsilon =-N\frac{d \phi}{d t}=NBa^{2}\omega sin \omega t$
$\epsilon =10Ba^{2}\omega sin \omega t$