A circular coil of radius 10 cm, 500 turns and resistance `2 Omega` is placed with its place,perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through `180^@` in 0.25 sec . Estimate the magnitudes of the EMF and current induced in the coil .[horizontal component of the earth's magnetic field at the place is `3.0 times 10^-5 T`).

Explanation

Earth's magnetic field 'B'=`3.0 times 10^5 T`
Area of the coil =`pir^2=pi times 10^2 m^-2`.(radius =10 cm =`10^-1`m)
Initial flux through the coil
`Q_((i nitial))=BA costheta=(3.0 times10^-5)times(pitimes10^-2)timescos0^@=3pitimes10^-7wb`.
(since the plane of coil is perpendicular to the magnetic field, the angle is zero)
Final flux after rotation.
`Q_((i nitial))=BA costheta=3.0 times10^-5timespitimes10^-2timescos18^@=-3pitimes10^-7wb`
Total flux =`(3pi times 10^-7)-(-3pi times 10^-7)=6pi times 10^-7 wb`
`therefore` The flux of estimated emf in
`epsilon=N.(Deltaphi)/(Deltal)=500times(6pitimes10^-7)/0.25=3.8times10^-3V`
The value of estimated current is
`I=epsilon/R=(3.8times10^-3)/(2Omega)=1.9times10^-3A`.