A circular coil of radius 10 cm, 500 turns and resistance `2Omega` is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through `180^@` in 0.25 s. Estimate the magnitudes of the emf and current induced in the coil. Horizontal component of the earth's magnetic field at the place is `3.0xx10^(-5)` T.

Explanation

Initially:

`Phi_1=NBA_1costheta_1`
`=NBAcos 0^@ " " (because A_1=A)`
=NBA

`Phi_2=NBA_2costheta_2`
`=NBAcos180^@ (because A_2=A)`
=-NBA
Average induced emf in the coil,
`(epsilon)=-(DeltaPhi)/(Deltat)`
`therefore (epsilon)=-((Phi_2-Phi_1)/(Deltat))`
`=-((-NBA-NBA)/(Deltat))`
`=(2NBA)/(Deltat)`
`=(2NB(pir^2))/(Deltat)`
`=((2)(500)(3xx10^(-5))(3.14)(0.1)^2)/(0.25)`
`=3.768xx10^(-3)` V
Now, average induced current ,
`(I)=(epsilon)/R`
`therefore (I)=(3.768xx10^(-3))/2`
`therefore lt I gt = 1.884xx10^(-3)` A