Question

A coil of $1200$ turns and mean area of $500 cm ^{2}$ is held perpendicular to a uniform magnetic field of induction $4 \times 10^{-4} T$. The resistance of the coil is $20 \Omega$. When the coil is rotated through $180^{\circ}$ in the magnetic field in $0.1 s$ the average electric current (in $mA$ ) induced is:

• A. $12$
• B. $24$
• C. $36$
• D. $48$

Answer 1

Answer: (B)

Magnetic flux linked with the each turn of coil
$\phi_{1}=B A \,\,\,\,$ as coil is perpendicular to B)
On rotating coil through $180^{\circ}$,
Flux linked $\phi_{2}=-B A$
$\therefore $ Change in magnetic flux
$\Delta \phi=\phi_{2}-\phi_{1}=-2 B A$
So, emf induced in the coil
$e=-N \frac{\Delta \phi}{\Delta t}=\frac{2 N B A}{\Delta t}$
where, $N$ is the number of turns in the coil.
The current in the coil is given by:
$ i =\frac{e}{R}=\frac{2 N B A}{R \Delta t} $
$=\frac{2 \times 1200 \times 4 \times 10^{-4} \times 500 \times 10^{-4}}{20 \times 0.1} $
$=24 \times 10^{-3} A =24\, mA $