A square loop of wire with side length 10 cm is placed at angle of `45^(@)` with a magnetic field that changes uniformly from 0.1 T to zero in 0.7s. The induced current in the loop (its resistance is `1Omega`) is

Options

A. 1.0 mA
B. 2.5 mA
C. 3.5 mA
D. 4.0 mA

Answer

A

Explanation

Area of a square loop , `A = 10 cm xx 10cm`
`A = 100 cm^2 = 100 xx 10^(-4) m^2 = 10^(-2) m^2`
Initial megnetic flux linked with the loop
`phi_1 = B_1 A cos phi = 0.1 xx 10^(-2) xx cos 45^@ = (10^(-3))/(sqrt2) Wb`
Final magnetic flux linked with the loop
`phi_2 = 0 Wb (because B_2 = 0)`
The induced emf in the loop is
`epsi = - (dphi)/(dt) = - ((phi_2 - phi_2))/(t) = ((0-(10^(-3))/(sqrt2) ) )/(0.7) = 10^(-3) V`
The induced current in the loop is
`I = epsi/R = (10^(-3) V)/(1Omega) = 10^(-3) A = 1.0 mA`