A small circular loop of wire of radius a is located at the centre...

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}\cos \left(\omegat\right) .

The emf induced in the smaller inner loop is nearly:

Options

A $\pi{\mu}_{0}{I}_{0}\dfrac{{a}^{2}}{b}\omega sin \left(\omegat\right)$
B $\dfrac{\pi{\mu}_{0}{I}_{0}}{2} . \dfrac{{a}^{2}}{b}\omega cos \left(\omegat\right)$
C $\dfrac{\pi{\mu}_{0}{I}_{0}{b}^{2}}{a}\omega cos \left(\omegat\right)$
D $\dfrac{\pi{\mu}_{0}{I}_{0}}{2} . \dfrac{{a}^{2}}{b}\omega sin \left(\omegat\right)$

Correct answer

D. $\dfrac{\pi{\mu}_{0}{I}_{0}}{2} . \dfrac{{a}^{2}}{b}\omega sin \left(\omegat\right)$

Step-by-step solution

Induced emf,

$ε = \dfrac{MdI}{dt},$

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

$M = \dfrac{{\mu}_{0}\pi{a}^{2}}{2b}, ε = - M\dfrac{d}{dt} ( {I}_{0}cos\omegat )$

$c = M\omega{I}_{0}\sin \left(\omegat\right)$

$= \dfrac{{\mu}_{0}\pi{a}^{2}}{2b}\omega{I}_{0}sin \omegat$

Practice Electromagnetic Induction on Quantrex Academy →

More from Electromagnetic Induction

List-I contains four conducting loops lying in the XY plane, as shown in the figures. The… JEE Advanced 2026 A 30 cm long solenoid has 10 turns per cm and area of 5 cm ^2 . The current through the… JEE Main 2026 A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as B… JEE Main 2026 An inductor of inductance 10 mH having resistance of 100\,Ω is connected to battery of… JEE Main 2026 A metal rod of length L rotates about one end at origin with a uniform angular velocity ω… JEE Main 2026 A circular loop of radius 20 cm and resistance 2\ Ω is placed in a time varying magnetic… JEE Main 2026 In the given circuit below inductance values of L_1 , L_2 and L_3 are same. The magnetic… JEE Main 2026 A circular current loop of radius R is placed inside square loop of side length L (L >>… JEE Main 2026 Full Electromagnetic Induction list All JEE Main PYQs