Question

A rectangular coil of $100$ turns and size $0.1m\times 0.05$m 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. $0.5V$
• B. $\sqrt{3}V$
• C. $\sqrt{0.6}V$
• D. $\sqrt{6}V$

Answer 1

Answer: (A)

$0.5V$

Given : $N=100$ turns $\Delta t=0.05$ s

Change in magnetic field $\Delta B=0.1-0.05=0.05$ T

Area of coil $A=0.1\times 0.05=5\times {10}^{-3}$ $m^2$

Thus magnitude of change in flux $\Delta \varphi =A\Delta B=5\times {10}^{-3}\times 0.05=2.5\times {10}^{-4}$ $Wb$

$\therefore$ Emf induced $E=N\frac{\Delta \varphi }{\Delta t}$

$⟹$ $E=100\times \frac{2.5\times {10}^{-4}}{0.05}=0.5$ volts