Question

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

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

Answer 1

Answer: (C)

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