Question

A circular coil consists $70$ closely wound turns and has a radius of $10\, cm$. An externally produced magnetic field of magnitude $2 \times 10^{-3}\, T$ is applied perpendicular to the coil. The net flux through the coil is found to vanish when the current in the coilis $2.2\, A$. The inductance of the coil is

• A. $2\, mH$
• B. $3 \, mH$
• C. $4 \, mH$
• D. $1.5 \, mH$

Answer 1

Answer: (A)

Given, number of turns in the circular coil,
$N=70, r=10 cm =10^{-1} m $
$B=2 \times 10^{-3} T $
$\theta=0^{\circ}$
Magnetic flux, $\varphi=N B A \cos \theta$
$=70 \times 2 \times 10^{-3} \times \pi r^{2} \times \cos 0^{\circ}$
$=140 \pi \times 10^{-3} \times\left(10^{-1}\right)^{2}$
$=140 \pi \times 10^{-5} $
$=140 \times \frac{22}{7} \times 10^{-5}$
$=4.4 \times 10^{-3} Wb$
We know that,
$\phi=L I $
$L=\frac{\phi}{I}=\frac{4.4 \times 10^{-3}}{2.2}$
$=2 \times 10^{-3} H =2\,mH$