Question

A coil of resistance $40\Omega$ is connected to a galvanometer of $160\Omega$ resistance. The coil has radius of $6\text{mm}$ and $100\text{turns}$. This coil is placed between the poles of a magnet such that the magnetic field is perpendicular to plane of the coil. If the coil is dragged out of this magnetic field instantaneously, a total charge of $32\mu \text{C}$ flows through the galvanometer. The magnitude of magnetic field is:

• A. $6.55\text{T}$
• B. $5.66\text{T}$
• C. $0.655\text{T}$
• D. $0.566\text{T}$

Answer 1

The correct option is D $0.566\text{T}$

Flux linked with the coil, when the coil is placed between the poles of magnet is,

${\varphi }_1=NBA\cos 0^{\circ }$

${\varphi }_1=100\times B\times \pi \times (6\times {10}^{-3}{)}^2$

${\varphi }_1=36\pi B\times {10}^{-4}\text{Wb}$

When the coil is removed,

${\varphi }_2=0$

We know that,

$\Delta q=\frac{|\Delta \varphi |}{R_{net}}$

Here, $R_{net}=(160+40)\Omega$

$R_{net}=200\Omega$

$\therefore 32\times {10}^{-6}=\frac{36\pi B\times {10}^{-4}}{200}$

$\therefore B=0.566\text{T}$

Hence, option ($C$) is the correct answer.