A plane loop is shaped as two squares (Fig) and placed in a uniform magnetic field at right angle to the loop's plane. The magnetic induction varies with time as `B =B_(0) sin (omega)t, where B_(0) = 10 mT and (omega) = 100 rads^(-1)`. The wires do not touch at point A. If resistance per unit length of the loop is `50 m(Omega)// m`, then amplitude of current induced in the loop is

Explanation

The flat shape is made up of concentric loops, having different radii, varying from `0` to `a`.
Let us consider and elementary loop of radius `r`, then e.m.f induced due to the this loop
`= (-d(vec(B) - vec(S)))/(dt) = pi r^(2) B_(0) omega cos omega t`.
and the total induced e.m.f.,
`xi_(ind) = int_(0)^(a) (pi r^(2) B_(0) cos omega t) d N`, ......(1)
where `pi r^(2) omega cos omega t` is the contribution of one turn of radius `r` and `d N` is the number of turns in the interval `[r,r + dr]`.
So, `d N = ((N)/(a)) dr` ....(2)
From (1) and (2) `xi = int -(pi r^(2) B_(0) omega cos omega t) (N)/(a) dr = (pi B_(0) omega cos omega t N a^(2))/(3)`
Maximum value of e.m.f amplitude `xi_(max) = (1)/(3) pi B_(0) omega N a^(2)`