JEE Main 2017 · 8 Apr · Shift 1 · Physics Q20

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PhysicsSingle correct+4 / -1Question 20 of 90

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 $I=I_o\cos(\omega t)$ . The emf induced in the smaller inner loop is nearly :

\dfrac{\pi\mu_oI_o}2\cdot\dfrac{a^2}b\,\omega\sin(\omega t)

\dfrac{\pi\mu_oI_o}2\cdot\dfrac{a^2}b\,\omega\cos(\omega t)

\pi\mu_oI_o\dfrac{a^2}b\,\omega\sin(\omega t)

\dfrac{\pi\mu_oI_ob^2}a\,\omega\cos(\omega t)

Answer and worked solution

Official answer: A

The field at the centre of the large loop is $\dfrac{\mu_0I}{2b}$ , nearly uniform over the small loop:
$\Phi=\pi a^2\frac{\mu_0I_0\cos\omega t}{2b},\qquad\varepsilon=-\frac{d\Phi}{dt}=\frac{\pi\mu_0I_0}2\cdot\frac{a^2}b\,\omega\sin\omega t.$

Topics:Faraday's and Lenz's laws Biot-Savart law

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JEE Main 2017 · 8 Apr · Shift 1, Physics question 20