A circular coil of radius 10 cm, 500 turns and resistance 2 Omega is placed with its plane prependicular 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 magnitude of the e.m.f and current induced in the coil. Horizotal component of earth's magnetic field at the place is `3 xx 10^(-5) T`.

Explanation

Initial flux through the coil,
`Phi_(B(i n itial)=BAcos theta`
`=3.0xx10^(-5)xx(pixx10^(-2))xxcos0^(@)`
`=3pixx10^(-7)Wb`
Final flux after the rotation,
`Phi_(B(fi nal))=3.0xx10^(-5)xx(pixx10^(-2))xxcos180^(@)`
`= –3π × 10^(–7) Wb`
Therefore, estimated value of the induced emf is,
`epsi=N(DeltaPhi)/(Deltat)`
= 500xx(6pixx10^(–7))//0.25`
`=3.8xx10^(–3)V`
`I = epsi//R = 1.9xx10^(–3)`A
Note that the magnitudes of ε and I are the estimated values. Their instantaneous values are different and depend upon the speed of rotation at the particular instant.