A circular coil of radius 100cm, 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 magnitude of the emf and current induced in the coil.
[Horizontal component of the earth's magnetic field `= 3.0 xx10^(-5)T` ]

Explanation

Here, radius, r = 100 cm = 1 m
Number of turns, N = 500
Resistance, `R=2Omega`
Angular velocity, `omega =(180)/(0.25)`
Magnetic field, `B = 3 xx 10^(-5)T `
Now, emf induced in the coil,
`e = (Ndphi)/t = (NBA)/t = (NB pir^2)/(2pi//omega)`
`=1/2 NBr^2 omega = 1/2 xx 500 xx (3xx10^(-5)) xx (1)^(2)xx 180/(0.25)=5.4 V`
Current induced , `i=e/R = (5.4)/2 = 2.7 A`