A circular coil of radius 8.0 cm and 20 turns, is rotated about its vertical diameter with an angular speed of `50 rad s^(-1)` in a uniform horizontal magnetic field of magnitude `3.0xx10^(-2)T`. Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance `10 Omega` , calculate the maximum value of current in the coil. Calculate the average loss due to joule heating . Where does this power come from ?

Explanation

Given : `N=20 ,R 8 xx 10^(-2)m, omega =50 rad s^(-1), B=3xx10^(-2) T,"resistance" r=10 Omega`
`i_(max)= ? bar p= ? `
Magnetic flux, `Phi=BAN cos omegat,A=piR^2`
`=3xx10^(-2)xx3.14xx64xx10^(-4)xx20 cos omegat`
`Phi=0.01206 cos omegat`
`e=-(dPhi)/(dt)=-0.01206 omegasin omega t`
`e=-0.01206 xx50 sin omega t`
`e=-0.603 sin omegat`
`e_m=0.603V`
`i_m=(e_m)/r=(0.603)/(10)=6.03xx10^(-2)A`
Average emf over a complete cycle is zero.
Average power `=(e_mi_m)/2`
`=(0.603xx6.03xx10^(-2))/(2)W`
=0.018 W
`barp=1.8xx10^(-2)W`.
This power comes from the external rotor.