1. Tardigrade
  2. Question
  3. Physics
  4. A very long solenoid of radius R is carrying a current I(t)=(k t e)-a t(k>0), as a function of time (t ≥ 0) taken as a counter clockwise current to be positive. A circular conducting coil of radius 2 R is placed in the equatorial plane of the solenoid and concentric with the solenoid itself. Then the current induced in the outer coil is correctly shown as a function of time by which of the following graph:

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A very long solenoid of radius $R$ is carrying a current $I(t)=(k t e)^{-a t}(k>0)$, as a function of time $(t \geq 0)$ taken as a counter clockwise current to be positive. A circular conducting coil of radius $2 R$ is placed in the equatorial plane of the solenoid and concentric with the solenoid itself. Then the current induced in the outer coil is correctly shown as a function of time by which of the following graph:

NTA AbhyasNTA Abhyas 2022

Solution:

Solution

$i_{i n d} \propto-\frac{d i}{d t}=-\frac{d}{d t}\left((\alpha t e)^{-\beta t}\right) $
$=-(\alpha e)^{-\beta t}+(\alpha t e)^{-\beta t}(-\beta) $
$=-(\alpha e)^{-\beta t}(1-\beta t)$
Check value at $t=0$