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 loops are connected in such a way that if the current is clockwise in one, it is anticlockwise in the other. Hence the e.m.f in loop `b` opposes the e.m.f in loop `a`.
`e.m.f` in loop `a = (d)/(dt) (a^(2) B) = a^(2) (d)/(dt) (B_(0) sin omega t)`
Similarly, `e.m.f` in loop `b = b^(2) B_(0) omega cos omega t`.
Hence, net `e.m.f` in the circuit `= (a^(2) - b^(2)) B_(0) omega cos omega t`, as both the e.m.f's are in opposite sense, and resistance of the circuit `= 4(a + b) rho`
Therefore, the amplitude of the current
`= ((a^(2) - b^(2))B_(0) omega)/(4 (a + b) rho) = 0.5 A`.