First slide

Inductance

Question

A coil of wire having finite 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 I₁(t) starts flowing through the coil. If I₂(t) is the current induced in the ring and B(t) is the magnetic field at the axis of the coil due to I₁(t) then as a function of time (t > 0), the product I₂ (t) B(t)

Difficult

A

Increases with time
B

Decreases with time
C

Does not vary with time
D

Passes through a maximum

Solution

Using k₁, k₂ etc. as different constants, we have
$I_{1} (t) = k_{1} [1 - e^{- t / τ}], B (t) = k_{2} I_{1} (t)$
$I_{2} (t) = k_{3} \frac{dB (t)}{dt} = k_{4} e^{- t / τ}$
$I_{2} (t) B (t) = k_{b} [1 - e^{- t / τ}] [e^{- t / τ}]$
This quantity is zero for t = 0 and $t =\propto$ and positive for other value of t. It must, therefore, pass through a maximum.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App