Question

A conducting ring of certain resistance is falling towards a current carrying straight long conductor. The ring and conductor are in the same plane. Then

• A. induced current in the coil is zero.
• B. induced current in the coil is anticlockwise.
• C. induced current in the coil is clockwise.
• D. ring will come to rest.

Hint:

Lenz’s Law states that the direction of induced current will always oppose the change in magnetic flux. This helps determine the direction of the induced current in various electromagnetic situations.

Answer 1

The Correct Option is C

Step 1: Understanding the problem.
In this problem, a conducting ring is falling towards a long straight conductor that is carrying a current. According to Lenz's Law and the principles of electromagnetic induction, when a conductor (the ring in this case) moves towards a magnetic field created by another current-carrying conductor, it will experience a change in magnetic flux, which induces a current in the ring.
The induced current in the ring will always oppose the change in flux that caused it, as per Lenz's Law.

Step 2: Applying Lenz's Law.
Lenz’s Law states that the direction of the induced current will be such that it opposes the change in flux. Here, as the conducting ring is falling towards the current-carrying conductor, the magnetic field produced by the current-carrying conductor increases in strength at the location of the ring.

Step 3: Direction of the magnetic field.
The magnetic field produced by a long straight conductor is given by Ampère’s Law:
\[ B = \frac{\mu_0 I}{2\pi r}, \]
where:
- \( \mu_0 \) is the permeability of free space,
- \( I \) is the current in the conductor,
- \( r \) is the distance from the conductor.
As the ring moves towards the conductor, the magnetic field at the location of the ring increases.

Step 4: Induced current.
According to Lenz's Law, the induced current in the ring will create a magnetic field that opposes the increase in flux caused by the magnetic field of the current-carrying conductor.
This means that the induced current in the ring will generate a magnetic field that opposes the field produced by the conductor. To oppose the field, the induced current in the ring must flow in such a direction as to produce a magnetic field opposite to that of the conductor.

Step 5: Determining the direction of the induced current.
Using the right-hand rule for the magnetic field due to the current in the conductor, the field lines around the conductor will circle it in a counterclockwise direction. To oppose this, the induced current in the ring must flow in a clockwise direction (since the magnetic field generated by the clockwise current in the ring will be opposite to the field produced by the conductor).

Step 6: Conclusion.
Thus, the induced current in the coil will be clockwise to oppose the increasing magnetic flux.
Final Answer:
The induced current in the coil is:
\[ \boxed{\text{clockwise}}. \]