Question

Find the maximum emf induced.

Answer 1

The magnetic flux is given as

$\varphi =A\times B$

$\varphi =2\times {10}^{-4}\times 0.1\times \cos \left(2\times \pi \times 5\right)t$

$\varphi =2\times {10}^{-5}\cos \left(10\pi t\right)$

The emf induced is given as

$e=NBA$

$e=50\times \left(2\times {10}^{-5}\times \sin \left(10\pi t\right)\right)$

Time period is

$T=\frac{1}{5}=0.2\sec$

The emf induced in one full cycle is zero. So the maximum emf induced will be in half cycle

$e=\underset{0}{\overset{0.1}{\int }}{10}^{-3}\sin \left(10\pi t\right)$

Hence, the maximum induced emf is $2\times {10}^{-3}$.