A rectangular coil of 100 turns and size `0.1mxx0.05m` is placed perpendicular to a magnetic field of 0.1 T. If the field drops to 0.05 T in 0.05 s, the magnitude of the emf induced in the coil is

Options

A. 2
B. 3
C. 0.5
D. 6

Answer

C

Explanation

Here,
Area of coil, `A=0.1mxx0.05m=5xx10^(-3)m^(2)`
Number of turns, N=100
Initial flux linked with the coil
`phi_(1)=BAcostheta=0.1xx5xx10^(-3)costheta=5xx10^(-4)Wb`
Find flux linked with the coil
`phi_(2)=0.05xx5xx10^(-3)cos0^(@)=25xx10^(-5)Wb=2.5xx10^(-4)Wb`
The magnitude of induced emf in the coil is
`epsi=(N|Deltaphi|)/(Deltat)=(N|phi_(2)-phi_(1)|)/(t)=(100|2.5xx10^(_4)-5xx10^(-4)|)/(0.05)`
`=(100xx2.5xx10^(-4))/(0.05)V=0.5`