Question

The magnetic flux through a loop is varying according to a relation $\varphi =6t^2+7t+1$ where $\varphi$ is in milliweber and t is in second. What is the e.m.f. induced in the loop at $t=2$ second?

Answer 1

Magnetic flux through a loop $\varphi =6t^2+7t+1$ $mWb$

Thus rate of change on flux $\frac{d\varphi }{dt}=12t+7$

Magnitude of emf induced in the loop $E=\frac{d\varphi }{dt}$

$\therefore$ $E=12t+7$ mV

Emf induced in the loop at $t=2$ s, $E{|}_{t=2}=12\times 2+7$ mV

$⟹$ $E{|}_{t=2}=31$ mV