Question

A circular coil of area $0.1m^2$ having $200$ turns is placed in a magnetic field of $40T$. The plane of the coil makes $30^{\circ }$ with the field. If the field is removed for $0.1s$ then the induced emf in the coil is

• A. $4000V$
• B. $4000\sqrt{3}V$
• C. $2000V$
• D. $2000\sqrt{3}V$

Answer 1

Answer: (B)

Given, area of circular coil, $A=0.1m^2$
number of turns in the coil, $N=200$ turns
and magnetic field, $B=40T$
The angle between plane of the coil and magnetic field, $\theta =30^{\circ }$
$\therefore$ Flux associated with plane coil in uniform magnetic field is given as,
$\therefore {\varphi }_1=NBS\cos \theta \left(\because \theta =30^{\circ }\right)$
${\varphi }_1=NBS\cos \theta$
$S=$ Area of surface
${\varphi }_1=200\times 40\times 0.1\times \cos 30^{\circ }$
$\theta =$ angle between the direction of magnetic field and normal to the surface.
$=200\times 40\times 0.1\times \frac{\sqrt{3}}{2}$
${\varphi }_1=400\sqrt{3}$
When, field removed for $0.1$ sec then the flux,
${\varphi }_2=0$
Net flux, $d\varphi ={\varphi }_1-{\varphi }_2=400\sqrt{3}$ and $dt=0.1sec$
Now, induced emf in the coil when field is removed for $0.1$ sec is
$\therefore E=\frac{d\varphi }{dt}=\frac{400\sqrt{3}}{0.1}$
or $E=4000\sqrt{3}V$