A circular coil of radius 10 cm, 500 turns and resistance `2 Omega` 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 `3.0 ×x 10^(-5)` T.

Explanation

Initial flux through the coil,
`Phi_(B("initial")) = BA cos theta `
`=3.0 xx 10^(-5) xx (pi xx 10^(-2)) xx cos 0^@`
`=3pi xx 10^(-7)` Wb
Final flux after the rotation.
`Phi_(B("final")) = 3.0 xx 10^(-5) xx (pi xx 10^(-2)) xx cos 180^@ `
`= - 3pi xx 10^(-7)` Wb
Therefore, estimated value of the induced emf is ,
`epsi =N (Delta Phi)/(Deltat)`
`= 500 xx (6 pi xx 10^(-7)) //0.25`
`= 3.8 xx 10^(-3) V`
`I = epsi//R = 1.9 xx 10^(-3) A `
Note that the magnitudes of `epsi` and I are the estimated values. Their instantaneous values are different and depend upon the speed of rotation at the particular instant.