Question 127: Electromagnetic Induction

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

Accepted Answer

Mutual inductance,
M = $${{{\mu _0}\pi {N_1}{N_2}\,{a^2}} \over {2b}}$$
here $${{N_1}}$$ = N
2
= 1
$$	herefore\,\,\,$$ M = $${{{\mu _0}\pi {a^2}} \over {2b}}$$
Current I = I
0
cos ($$\omega $$t)
According to Faraday's law,
e = $$-$$ M $${{dI} \over {dt}}$$
= $$-$$ $${{{\mu _0}\pi {a^2}} \over {2b}}$$  $${d \over {dt}}$$ (I
0
cos $$\omega $$t)
= + $${{{\mu _0}\pi {a^2}} \over {2b}}$$ I
0
$$\omega $$ sin $$\omega $$t
= $${{\pi {\mu _0}{I_0}} \over 2}$$ . $${{{a^2}} \over b}$$ $$\omega $$ sin $$\omega $$ t

Answer

$${{\pi {\mu _o}{I_o}} \over 2}.{{{a^2}} \over b}\,\omega \sin \left( {\omega t} \right)$$

Answer

$${{\pi {\mu _o}{I_o}} \over 2}.{{{a^2}} \over b}\,\omega \cos \left( {\omega t} \right)$$

Answer

$$\pi {\mu _o}{I_o}\,{{{a^2}} \over b}\omega \sin \left( {\omega t} \right)$$

Answer

$${{\pi {\mu _o}{I_o}\,{b^2}} \over a}\omega \cos \left( {\omega t} \right)$$

Electromagnetic Induction

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

Choose the correct answer: