Question

A circular coil of wire consists of exactly 100 turns with a total resistance 0.20$\mathrm{\Omega}$. The area of the coil is 100 cm^{2}. The coil is kept in a uniform magnetic field B as shown in figure. The magnetic field is increased at a constant rate of 2 T s^{-1}. Find the induced current in the coil in A.

Moderate

Solution

The total flux through N turns of the coil,

${\mathrm{\varphi}}_{\mathrm{total}}=\mathrm{NBAcos\theta}$

According to Faraday's law of electromagnetic induction,

${\mathrm{E}}_{\mathrm{induced}}=-\frac{\mathrm{d\varphi}}{\mathrm{dt}}=-\frac{\mathrm{d}}{\mathrm{dt}}\left(\mathrm{NBAcos\theta}\right)\phantom{\rule{0ex}{0ex}}=-\left(\mathrm{NAcos\theta}\right)\frac{\mathrm{dB}}{\mathrm{dt}}$

The current induced in the coil,

${\mathrm{I}}_{\mathrm{induced}}=\frac{{\mathrm{E}}_{\mathrm{induced}}}{\mathrm{R}}=5\mathrm{A}$

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An elasticized conducting band *r* is around a spherical balloon T (figure). Its plane passes through the center of the balloon. A uniform magnetic field of magnitude 0.04 T is directed perpendicular to the plane of the band. Air is let out of the balloon at 100 cm^{3}s^{-1} at an instant when the radius of the balloon is 10 cm. The induced emf in the band is

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