A small circular loop of wire… - JEE Main 2017 Physics PYQ

JEE Main 2017 — Physics Electromagnetism

2017mcqmedium

A small circular loop of wire of radius $a$ is located at the centre of a much larger circular wire loop of radius $b$ . The two loops are in the same plane. The outer loop of radius $b$ carries an alternating current $I={I}_{0}\mathrm{cos}⁡(\omega t).$ The emf induced in the smaller inner loop is nearly:

Official previous-year question

Held on 8 Apr 2017 · Verified 6 Jul 2026.

Options

A
$\pi {\mu }_{0} {I}_{0}\frac{{a}^{2}}{b}\omega \mathrm{sin}(\omega t)$
B
$\frac{\pi {\mu }_{0} {I}_{0}}{2} .\frac{{a}^{2}}{b} \omega \mathrm{cos}(\omega t)$
C
$\frac{\pi {\mu }_{0} {I}_{0} {b}^{2}}{a}\omega \mathrm{cos}(\omega t)$
D
$\frac{\pi {\mu }_{0} {I}_{0}}{2} .\frac{{a}^{2}}{b}\omega \mathrm{sin}(\omega t)$

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Solution

Induced emf,

$\epsilon =\frac{MdI}{dt},$

Current is given as, $I={I}_{0}cos\omega t$

$M=\frac{{\mu }_{0}\pi {a}^{2}}{2b}, \epsilon =-M\frac{d}{dt} ({I}_{0}\mathrm{cos}\omega t)$

$c=M \omega {I}_{0} \mathrm{sin}(\omega t)$

$=\frac{{\mu }_{0}\pi {a}^{2}}{2b}\omega {I}_{0}\mathrm{sin}⁡ \omega t$

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Options

$\pi {\mu }_{0} {I}_{0}\frac{{a}^{2}}{b}\omega \mathrm{sin}(\omega t)$

$\frac{\pi {\mu }_{0} {I}_{0}}{2} .\frac{{a}^{2}}{b} \omega \mathrm{cos}(\omega t)$

$\frac{\pi {\mu }_{0} {I}_{0} {b}^{2}}{a}\omega \mathrm{cos}(\omega t)$

$\frac{\pi {\mu }_{0} {I}_{0}}{2} .\frac{{a}^{2}}{b}\omega \mathrm{sin}(\omega t)$

Solution

Induced emf,

$\epsilon =\frac{MdI}{dt},$

Current is given as, $I={I}_{0}cos\omega t$

$M=\frac{{\mu }_{0}\pi {a}^{2}}{2b}, \epsilon =-M\frac{d}{dt} ({I}_{0}\mathrm{cos}\omega t)$

$c=M \omega {I}_{0} \mathrm{sin}(\omega t)$

$=\frac{{\mu }_{0}\pi {a}^{2}}{2b}\omega {I}_{0}\mathrm{sin}⁡ \omega t$

Options

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Solution

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Options

Did you get this right?

Solution

Your note

JEE Main Electromagnetism in other years

More JEE Main Electromagnetism questions

Other Physics topics for JEE Main

Mechanics

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Electromagnetism