A semicircular wire of radius r is rotating with angular velocity `omega` in a uniform magnetic field B with its radius as axis. If the resistance of the circuit be R and if the axis of rotation remains perpendicular to B, what will be the average power produced in each period?

Explanation

Magnetic flux, `phi=BAcosomegat=B.(pir^(2))/(2).cosomegat`
`therefore` emf induced, `e=-(dphi)/(dt)=(Bpir^(2))/(2)omegasinomegat`
Power, `P=(e^(2))/(R)=((Bpir^(2)omega)^(2))/(4R)sin^(2)omegat`
In a complete period, the average of `sin^(2)omegat=(1)/(2)`
So, the average power, `barP=((Bpir^(2)omega)^(2))/(8R)`