A metal coil of area `5 xx 10^(-3)m^(2)`, number of turns 100 and resistance `0.5 Omega` is lying horizontally at the bottom of a vessel made of an insultating material. A uniform magnetic field passing vertically through the coil changes from 0 to 0.8t in 0.2 s. What is induced current (in ampere) flowing through the coil?

Options

A. 2A
B. 3A
C. 4A
D. 5A

Answer

C

Explanation

The magnetic flux `phi = NAB`
`:.` The induced e.m.f. = `e = -(d phi)/(dt)`
`:. |e| = |(d phi)/(dt)| = NA (dB)/(dt)`
But (`dB)/(dt) = 0.8/0.2 = 4 T//s`
`:. e = NA(dB)/(dt)=100 xx 5 xx 10^(-3) xx 4 :. e = 2 V`
`:.` induced current `I = e/R = 2/0.5 = 4 A`.