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A ring rotates with angular velocity ome...

A ring rotates with angular velocity `omega` about an axis in the plane of the ring which passes through the center of the ring. A constant magnetic field `B` exists perpendicualr to the plane of the ring . Find the emf induced in the ring as a function of time.

Text Solution

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At any time, `phi=BA cos theta =BA cos omega t`
Now induced emf in the loop

`e=(-dphi)/(dt)=BA omega sin omega t `
If there are N turns.
emf`=BA omegaN sin omegat`
`BA omegaN` is the amplitude of the emf
`e=e_(m)sin omegat`
`i=( e)/( R)=(e_(m))/( R) sin wt=i_(m) sin wt `
`i_(m)=(e_(m))/( R)`
The rotating coil thus produces a sinusoidally varying current or alternating current. This is also the principle used in generator.
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