Question

The magnetic flux $\left(\varphi \right)$ through a coil varies with time $t$ as shown in the diagram. Which graph best represents the variation of the e.m.f $E$ induced in the coil with time $t$ ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

From the figure we can say that,

The graph of magnetic flux is a sine curve.

Therefore, the magnetic flux through the coil is given by,

$\varphi ={\varphi }_0\sin \omega t$

Where, ${\varphi }_0$ is the maximum value of magnetic flux.

$\therefore$ the emf generated in the coil is given by:

$E=-\frac{d\varphi }{dt}$

$E=-\frac{d}{dt}\left({\varphi }_0\sin \omega t\right)$

$\Rightarrow E=-{\varphi }_0\omega \cos \omega t$

Therefore, the graph of emf generated will be as shown below.



The peak value of e.m.f is given by,

$E_0=\pm {\varphi }_0\omega$

Hence, option $\left(C\right)$ is the correct answer.