Q

# Solve! At the centre of a fixed large circular coil of radius R, a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate with a

At the centre of a fixed large circular coil of radius R, a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity ω about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time t of its start of rotation.

• Option 1)

$\frac{\mu _{0}I}{2R}\omega \pi r^{2}sin\omega t$

• Option 2)

$\frac{\mu _{0}I}{4R}\omega \pi r^{2}sin\omega t$

• Option 3)

$\frac{\mu _{0}I}{4R}\omega r^{2}sin\omega t$

• Option 4)

$\frac{\mu _{0}I}{2R}\omega r^{2}sin\omega t$

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As we learnt

Magnetic field due to cCrcular Current Carrying arc -

$B=\frac{\mu_{o}}{4\pi}\:\frac{2\pi i}{r}=\frac{\mu_{o}i}{2r}$

- wherein

Magnetic field due to cCrcular Current Carrying arc -

$B=\frac{\mu_{o}}{4\pi}\:\frac{2\pi i}{r}=\frac{\mu_{o}i}{2r}$

- wherein

$B=\frac{\mu _{0}I}{2R}$

At time the samller coil is rotated by $\omega t$

Angle between $\overrightarrow{B} \: \: and \: \: \overrightarrow{A} = \omega t$

$\therefore \phi =BAcos\omega t=\left ( \frac{\mu _{0}I}{2R} \right )\Pi r^{2}.cos\omega t$

$\therefore EMF=\left | -\frac{\mathrm{d} \phi }{\mathrm{d} t} \right |=\frac{\mu _{0}I.\Pi r^{2}\omega }{2R}sin\omega t$

Option 1)

$\frac{\mu _{0}I}{2R}\omega \pi r^{2}sin\omega t$

Option 2)

$\frac{\mu _{0}I}{4R}\omega \pi r^{2}sin\omega t$

Option 3)

$\frac{\mu _{0}I}{4R}\omega r^{2}sin\omega t$

Option 4)

$\frac{\mu _{0}I}{2R}\omega r^{2}sin\omega t$

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