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In a uniform magnetic field of induced B...

In a uniform magnetic field of induced `B`, a wire in the form of a semicircle of radius `r` rotates about the diameter of the circle with an angular frequency `omega`. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is `R`, the mean power generated per period of rotation is

A

`(Bpir^(2)omega)/(2R)`

B

`((Bpir^(2)omega)^(2))/(8R)`

C

`((Bpiromega)^(2))/(2R)`

D

`((Bpiromega^(2))^(2))/(8R)`

Text Solution

Verified by Experts

The correct Answer is:
B
`phi=B(pi r^(2))/(2)cos omegat`
`:. epsi=-(dphi)/(dt)=(1)/(2) B pi r^(2) omega sin omegat`
`:.P=epsi^(2)/(R)=(B^(2)pi^(2)r^(4)omega^(2)sin^(2)omegat)/(4R)`
`:. ltPgt=((Bpir^(2)omega)^(2))/(8R)" " ( :.ltsin^(2)omegatgt=(1)/(2))`
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