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 `10Omega`, calculate teh maximum value of current in the coil Calculated the average power loss due to Joule heating. Where does this power come from?

Explanation

For a coil rotating in a magnetic field, `varepsilon=-BANomegasinomegat`
`varepsilon_(max)=-BANomega` (numerically)
Here `B=3xx10^(-2)T,A=pir^(2)=pixx(8xx10^(-2))^(2)`
`N=20,omega=50" rad "s^(-1)`
`varepsilon_(max)=20xx50xxpixx64xx10^(-4)xx3xx10^(-2)=0.603V`
`varepsilon_("average")` over a cycle is zero
`I_(max)=(varepsilon_(max))/(R)=(0.603)/(10)=0.0603A`
`P_("average")=(1)/(2)varepsilon_(max)I_(max)=(1)/(2)xx0.603xx0.0603=0.018W`
Source of power loss is the external rotor which provides the necessary torque.