Question

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

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

Answer 1

Answer: (B)

Given, area of circular coil, $A=0.1 \,m ^{2}$
number of turns in the coil, $N=200$ turns
and magnetic field, $B=40\, T$
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,
$\therefore \phi_{1}=N B S \cos \theta \,\,\,\left(\because \theta=30^{\circ}\right)$
$\phi_{1} =N B S \cos \theta$
$S =$ Area of surface
$\phi_{1} =200 \times 40 \times 0.1 \times \cos 30^{\circ}$
$\theta=$ angle between the direction of magnetic field and normal to the surface.
$=200 \times 40 \times 0.1 \times \frac{\sqrt{3}}{2} $
$\phi_{1} =400 \sqrt{3}$
When, field removed for $0.1$ sec then the flux,
$\phi_{2}=0$
Net flux, $d \phi=\phi_{1}-\phi_{2}=400 \sqrt{3}$ and $d t=0.1 sec$
Now, induced emf in the coil when field is removed for $0.1$ sec is
$\therefore E=\frac{d \phi}{d t}=\frac{400 \sqrt{3}}{0.1}$
or $E=4000 \sqrt{3} \,V$