### JEE Main On 8 April 2017 Question 22

##### Question: 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 (\omega t). $ The emf induced in the smaller inner loop is nearly? [JEE Online 08-04-2017]

#### Options:

A) $ \pi {\mu_0}I _0\frac{a^{2}}{b}\omega \sin (\omega t) $

B) $ \frac{\pi {\mu_0}I _0}{2}.\frac{a^{2}}{b}\omega \cos (\omega t) $

C) $ \frac{\pi {\mu_0}I _0b^{2}}{a}\omega \cos (\omega t) $

D) $ \frac{\pi {\mu_0}I _0}{2}.\frac{a^{2}}{b}\omega \sin (\omega t) $

## Show Answer

#### Answer:

Correct Answer: D

#### Solution:

- e = MdI dT $ M=\frac{\pi {\mu_0}a^{2}}{2b} $ $ =\frac{\pi {\mu_0}a^{2}}{2b}=\omega I _0l\omega t $