Question

A loop of wire enclosing an area $S$ is placed in a region where the magnetic field is perpendicular to the plane. The magnetic field $\overrightarrow{B}$ varies with the time according to the expression $B=B_0{e}^{-at}$ where $a$ is some constant emf in the loop as a function of time. Calculate the induced emf?

• A. $e=2aS{B}_0{e}^{-at}$
• B. $e=6aS{B}_0{e}^{-at}$
• C. $e=7aS{B}_0{e}^{-at}$
• D. $e=aS{B}_0{e}^{-at}$

Answer 1

The correct option is D $e=aS{B}_0{e}^{-at}$

Magnetic field is given, $B=B_0{e}^{-at}$

So, the magnetic flux $\varphi =BS=B_{0}S{e}^{-at}$

Hence, induced emf $e=-\frac{d\varphi }{dt}=-B_{0}S(-a)e^{-AT}=aS{B}_0{e}^{-at}$