Question

Two different loops are concentric \(\&\) lie in the same plane. The current in outer loop is clockwise \& increasing with time. The induced current in the inner loop then, is ....... (a) clockwise (b) zero (c) counter clockwise (d) direction depends on the ratio of loop radii

Short answer

The direction of the induced current in the inner loop is counter-clockwise (c).

Step-by-step solution

Recognize the concepts involved in the problem

To solve this problem, we will use Faraday's Law of Electromagnetic Induction and Lenz's Law. Faraday's Law states that a change in the magnetic field across a coil will induce an electromotive force (induced voltage) in the coil, which in turn causes current to flow if there is a closed path. Lenz's Law tells us the direction of the induced current, which is such that it opposes the change in the magnetic field that caused it.

Analyze the behavior of the magnetic field

Since the current in the outer loop is increasing and clockwise, the magnetic field generated by the outer loop at the position of the inner loop is also increasing. The magnetic field lines created by a circular loop will form concentric circles around it. The direction of the magnetic field can be determined by the right-hand rule: for a clockwise current, the field lines will point towards the center of the loop.

Apply Lenz's Law to the problem

Now we need to find the direction of the induced current in the inner loop. Lenz's Law states that the induced current will flow in such a way that its magnetic field opposes the change in the magnetic field that caused it. In our case, the magnetic field from the outer loop is increasing and pointing towards the center of the loops. So, the induced current in the inner loop will create a magnetic field that opposes the increase, i.e., it will have a direction such that its magnetic field points outward, away from the center of the loops.

Determine the direction of the induced current in the inner loop using the right-hand rule

We use the right-hand rule again, but this time to determine the direction of the induced current in the inner loop that generates a magnetic field pointing outward. To do this, curl your right-hand fingers in the direction of the desired magnetic field (outward), and your extended thumb will indicate the direction of the induced current. In this case, the induced current in the inner loop will be counter-clockwise. Solution: The direction of the induced current in the inner loop is counter-clockwise (c).