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

Options

A. `(Bpir^(2)omega)/(2R)`
B. `((Bpir^(2)omega)^(2))/(8R)`
C. `((Bpiromega)^(2))/(2R)`
D. `((Bpiromega^(2))^(2))/(8R)`

Answer

B

Explanation

`e = NABomega sin omegat`
`P = (e^(2))/(R) = ((ABomega)^(2) sin^(2) omegat)/(R)`
`lt P gt = ((ABomega)^(2))/(R) lt sin^(2)omega gt`
`= (((pir^(2))/(2) Bomega)^(2) xx (1)/(2))/(R) = ((pir^(2)Bomega)^(2))/(8R)`