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 the vertical diameter through `180^@` in 0.25 s. Estimate the magnitude of emf and current induced in the coil.
[Take, `H = 3 xx10^(-5) T` ]

Explanation

Here, radius, r = 10 cm = 0.1 m
Number of turns, N = 500
Resistance, `R=2Omega`
Magnetic field, `B = 3xx10^(-5)T`
Area of loop, `A=pir^(2) = pi xx (0.1)^2`
`implies A=0.0314 m^(2)`
Initial flux, `phi_1 = BA cos 0^@ = BA`
Final flux, `phi_f = BA cos 180^@=-BA`
Magnitude of change in flux,
`|Deltaphi|=2BA`
`:. |Deltaphi|=2 xx3 xx10^(-5) xx0.0314`
`= 1.88xx10^(-6)`
`:.` Magnitude of emf induced,
`epsilon=(|Deltaphi|)/(Deltat)`
`implies epsilon= (1.88xx10^(-6))/(0.25) (Deltat = 0.25s)`
`implies epsilon = 7.54 xx10^(-6)V`
Magnitude of current induced,
`I=(epsilon)/R = (7.54xx10^(-6))/(2)`
`= 3.77 xx10^(-6)A`