Question

A rectangular coil 100 turns and size $0.1m\times 0.05m$ is placed perpendicular to a magnetic field of 0.1 T. If the field drops to 0.05 T in 0.05 second, the magnitude of the e.m.f. induced in the coil is

• A. 2
• B. 3
• C. 0.5
• D. 6

Answer 1

Answer: (C)

0.5

Here area of coil, $A=0.1m\times 0.05m=5\times {10}^{-3}{m}^2$
Number of turns, $N=100$

Initial flux linked with the coil
${\varphi }_1$ $=BAcos\theta =0.1\times 5\times {10}^{-3}cos{0}^o=5\times {10}^{-4}Wb$

The magnitude ot induced emf in the coil is:

$ϵ=\frac{n|\Delta \varphi |}{\Delta t}=\frac{N({\varphi }_2-{\varphi }_1)}{t}$

$=100\times \frac{2.5\times {10}^{-4}-5\times {10}^{-4}}{0.05}$

$=100\times \frac{|2.5\times {10}^{-4}|}{0.05}$

$=0.5V$