A conducting loop (as shown) has total resistance R . A uniform magnetic field B = γ t is applied perpendicular to plane of the loop where γ is a constant and t is time. The induced current flowing through loop is

Step-by-step solution

Given, Uniform magnetic field B = γ t Total flux, B 1 → . A 1 → + B 2 → . A 2 → = B b 2 cos ⁡ 0 o + B a 2 cos ⁡ 180 o = B b 2 - B a 2 ϕ = B ( b 2 - a 2 ) ϕ = γ t ( b 2 - a 2 ) We know that, Induced current (i) = e R = d ϕ d t R From Equation (i), i = d d t [ γ t b 2 - a 2 ] R i = b 2 - a 2 γ R