A rectangular coil of 100 turns and size `0.1 m xx 0.05 m` is placed perpendicular to a magnetic field of 0.1 T. If the field drops to 0.05 T in 0.05 second, the magnitude o the e.m.f. induced in the coil is

Options

A. `sqrt(2)`
B. `sqrt(3)`
C. `sqrt(0.6)`
D. None of the above

Explanation

Here, Area of coil, `A= 0.1 m xx 0.05 m = 5 xx 10^(-3) m^(2)`
Number of turns, N = 100
Initial flux linked with the coil
`phi_(1) = BA cos theta = 0.1 xx 5 xx 10^(-3) cos 0^(@)`
`=5 xx 10^(-4)Wb`
Final flux linked with the coil
`phi_(2) = 0.05 xx 5 xx 10^(-3) cos 0^(@)`
`=5 xx 10^(-4)Wb`
Final flux linked with the coil
`phi_(2) = 0.05 xx 5 xx 10^(-3) cos 0^(@)`
`=25 xx 10^(-5) Wb = 2.5 xx 10^(-4)wb`
The magnitude of induced emf in the coil is
`epsi = (N|Delta phi|)/(Delta t) = (N|phi_(2) - phi_(1)|)/(t)`
`= (100|2.5 xx 10^(-4) -5 xx 10^(-4)|)/(0.05)`
`= (100 xx 2.5 xx 10^(-4))/(0.05) V= 0.5V`
None of the given options is correct