# 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 : Option 1) Option 2) Option 3) Option 4)

As we learnt in

IF Magnetic field (B) — change -

$\varepsilon = -NA\cos \Theta \left ( \frac{dB}{dt} \right )$

- Magnetic field produced by outer loop = $\frac{\mu _{o}I}{}{2R} = \frac{\mu _{o}I_{o}cos\omega t}{2b}$

$\phi = B.A = (\frac{\mu _{o}I_{o}coswt}{2b}) \pi a^{2}$

$\xi = \left | \frac{-dL}{dt} \right | = \frac{\mu _{o}I_{o}\pi }{2b} a^{2} . \omega\:sin \omega t$

Option 1)

This option is correct.

Option 2)

This option is incorrect.

Option 3)

This option is incorrect.

Option 4)

This option is incorrect.

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