Question

The magnetic flux linked with a coil is $\varphi$ and the EMF induced in it is $E$ , then

• A. If $\varphi =0$ , $E$ must be $0$
• B. If $\varphi \ne 0$ , $E$ cannot be zero
• C. If $E$ is not $0$ , $\varphi$ may or may not be $0$
• D. none of the above is correct

Answer 1

Answer: (C)

Induced emf,
$E=-\frac{d\varphi }{dt}$
Therefore, $E=0$ when $\frac{d\varphi }{dt}=0$ and vice versa.
Even if $\varphi =0,\frac{d\varphi }{dt}$ may be non-zero.
Similarly, if $\varphi \ne 0,\frac{d\varphi }{dt}$ may be zero.
For example, if $\varphi ={\left(\varphi \right)}_{0}sin\left(\omega t\right)$
Then, $E=-\frac{d\varphi }{dt}=-{\left(\varphi \right)}_{0}cos\left(\omega t\right)$