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 :

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 (ω t). The emf induced in the smaller inner loop is nearly : (A) (πμo Io/2) . (a2/b) ω sin(ω t ) (B) (πμo Io/2) . (a2/b) ω cos (ω t ) (C) πμo Io . (a2/b) ω sin(ω t ) (D) (πμo Io b2/a) . ω cos (ω t )

Tardigrade Admin · Accepted Answer

e = MdI dT M = (μ0π a2/2b) = (μ0π a2/2b) = ω I0 lω t

Q. 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 $I = I_{o} cos (ω t)$ . The emf induced in the smaller inner loop is nearly :

$\frac{π μ _{o} I _{o}}{2} . \frac{a ^{2}}{b} ω sin (ω t)$

$\frac{π μ _{o} I _{o}}{2} . \frac{a ^{2}}{b} ω cos (ω t)$

$π μ_{o} I_{o} . \frac{a ^{2}}{b} ω sin (ω t)$

$\frac{π μ _{o} I _{o} b ^{2}}{a} . ω cos (ω t)$

$e = M d I$
$d T M = \frac{μ _{0} π a ^{2}}{2 b}$
$= \frac{μ _{0} π a ^{2}}{2 b} = ω I_{0} l ω t$

Q. 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(ωt). The emf induced in the smaller inner loop is nearly :

2πμo​Io​​.ba2​ωsin(ωt)

2πμo​Io​​.ba2​ωcos(ωt)

πμo​Io​.ba2​ωsin(ωt)

aπμo​Io​b2​.ωcos(ωt)