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. Increase 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_(2)I_(1)(t)`
`I_(2)(t)`
`I_(2)(t)=k_(3)(dB(t))/(dt)=k_(4)e^(-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=prop` and positive for other value of `t`. It must, therefore, pass through a maximum.