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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

 
Answers (1)
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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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