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11. (JEE Main 2017 (Online) 8th April Morning Slot)

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 = Io cos ( ω t). The emf induced in the smaller inner loop is nearly :

A. π μ o I o 2 . a 2 b ω sin ⁡ ( ω t )

B. π μ o I o 2 . a 2 b ω sin ⁡ ( ω t )

C. π μ o I o a 2 b ω sin ⁡ ( ω t )

D. π μ o I o b 2 a ω cos ⁡ ( ω t )

Correct option is (A)

Mutual inductance,

M = μ 0 π N 1 N 2 a 2 2 b

here N 1 = N2 = 1

∴ M = μ 0 π a 2 2 b

Current I = I0 cos ( ω t)

According to Faraday's law,

e = − M d I d t

= − μ 0 π a 2 2 b d d t (I0 cos ω t)

= + μ 0 π a 2 2 b I0 ω sin ω t

= π μ 0 I 0 2 . a 2 b ω sin ω t

12. (AIEEE 2008)

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area A = 10 c m 2 and length = 20 c m . If one of the solenoid has 300 turns and the other 400 turns, their mutual inductance is
( μ 0 = 4 π × 10 − 7 T m A − 1 )

A. 2.4 π × 10 − 5 H

B. 4.8 π × 10 − 4 H

C. 4.8 π × 10 − 5 H

D. 2.4 π × 10 − 4 H

Correct option is (D)

M = μ 0 N 1 N 2 A ℓ

= 4 π × 10 − 7 × 300 × 400 × 100 × 10 − 4 0.2

= 2.4 π × 10 − 4 H

13. (AIEEE 2006)

Which of the following units denotes the dimension M L 2 Q 2 , where Q denotes the electric charge?

A. W b / m 2

B.Henry ( H )

C. H / m 2

D.Weber ( W b )

Correct option is (B)

Mutual inductance = ϕ I = B A I

[Henry] = [ M T − 1 Q − 1 L 2 ] [ Q T − 1 ] = M L 2 Q − 2