A coil of wire having finite inductance and resistance has a conducting ring placed coaxially within it. The coil is connected a battery at time t = 0 , so that a time dependent current $I_1(t)$ starts flowing through the coil. If $I_2(t)$ is the current induced in the ring and B (t) is the magnetic field at the axis of the coil dut to $I_1(t)$ then as a function of time (t > 0), the product $I_2(t) \,B(t)$