A coil of wire having inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time t=0, so that a time-dependent current `1_(1)(t)` starts following 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 due to `I_(1)(t)` then as a function of time `(tgt0)`, the product `I_(2)(t)B(t)`

Options

A. Increases with time
B. Decreases with time
C. Does not vary with time
D. Passes through a maximum

Answer

D

Explanation

Using `k_1, k_2` etc, as different constants.
`I_1(t)=k_1[1-e^(-t//tau)]B(t)=k_2I_1(t)`
`I_2(t) =k_3(dB(t))/(dt)=k_4e^(-t//tau)`
`:. I_2(t)B(t)=k_5[1-e^(-t//tau)][e^(-t//tau)]`

This quantity is zero for t = 0 and `t = oo` and positive for other values of t. It must, therefore, pass through a maximum .