Question

Two different loops are concentric and lie in the same plane. The current in the outer loop is clockwise and increases with time. The induced current in the inner loop then is?

• A. clockwise
• B. zero
• C. counter clockwise
• D. in a direction that depends on the ratio of the loop radii

Answer 1

The correct option is C

counter clockwise

Step 1: Given data

A current is flowing clockwise and increasing with time in the outer loop.

Step 2: Formula used

Due to electromagnetic induction, an alternating emf ($\epsilon$) hence current will induce in the inner coil as the current is changing at the outer coil.

Now according to the Lenz law, the induced emf ($\epsilon$) will produce in such a way that the current whose magnetic field will oppose the change in magnetic flux.

$\begin{array}{rcl}\epsilon & =& -\frac{d\varphi }{dt}\end{array}$

Step 3: Calculation

We can write,

$\begin{array}{rcl}IR& =& -\frac{d\varphi }{dt}whereI,Rarecurrentandresis\tan e,\varphi istheelectricflux\\ I& =& \frac{-1}{R}\frac{d\varphi }{dt}\end{array}$

Hence, the current will be induced in the counter-clockwise direction for the inner loop.

Therefore, option (C) is the correct answer.