Question

A conduction loop of area $5$$c{m}^2$ is placed in a magnetic field which varies sinusoidally with time as $B=0.2\sin 300t$. The normal to the coil makes an angle of ${60}^o$ with the field. The emf induced at $t=\left(\pi /900\right)$s is?

• A. $7.5\times {10}^{-3}$V
• B. Zero
• C. $15\times {10}^{-3}$V
• D. $20\times {10}^{-3}$V

Answer 1

Answer: (A)

$7.5\times {10}^{-3}$V

$\varphi =BA\cos \theta$
$=0.2\sin \left(300t\right)\times 5\times {10}^{-4}\times \cos {60}^o$
$=5\times {10}^{-5}\sin \left(300t\right)$
$\therefore e=\frac{d\varphi }{dt}$
$=5\times {10}^{-5}\times 300\cos \left(300t\right)$
$=1.5\times {10}^{-2}\cos (300\times \frac{\pi }{900})$
$=1.5\times {10}^{-2}\cos \left(\frac{\pi }{3}\right)$
$=0.75\times {10}^{-2}$
$=7.5\times {10}^{-3}$V.