Question

A circular coil consists $70$ closely wound turns and has a radius of $10cm$. 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 $2.2A$. The inductance of the coil is

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

Answer 1

Answer: (A)

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