A coil is rotating in a uniform magnetic field with a angular velocity `omega`. Prove that maximum power consumed in the circuit is
`P = (N^(2)B^(2)A^(2)omega^(2))/(R )`

Explanation

Power consumed by rolating coil in external magnetic field.
Let the area of coil be A.
the number of turns of coil be N,
megnetic field be B.
According to the question.
if at any instant, the coil makes an angle `theta` with magnetic field B.
So, megnetic flux `phi = NBA cos phi ("as" phi = omega t)`
So, `" " phi = NBA cos omega t`
`[omega = "angular velocity"]`
As from Faraday.s law of electromagnetic induction emf indced
`e = -(dphi)/(dt) = - NBA(d)/(dt) cos omega t`
`= - NAB(-omega sin omega t)`
= `NAB omega sin omega t`
As we can say that from the expression of alternating voltage
`e = NAB omega sin omega t`
`NAB omega = e_(0)` = Peak voltage
So, power P is given by `=(e_(0)^(2))/(R) = (NAB omega^(2))/(R)`
`(N^(2)B^(2)A^(2)omega^(2))/(R)`