Question

A bar magnet falls from rest under gravity through the center of a horizontal ring of conducting wire as shown in the figure,

Which of the following graph best represents the speed (v) vs. time(t) graph of the bar magnet?

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is A

Explanation:
1. Initial Motion:
  - When the bar magnet is first released from rest, it starts to accelerate downward due to gravity.
  - The speed of the magnet increases as it falls freely.
2. Induced Current and Magnetic Field:
  - As the magnet approaches the ring, the changing magnetic flux through the ring induces a current in the wire (according to Faraday's Law of Electromagnetic Induction).
  - This induced current generates a magnetic field that opposes the motion of the falling magnet (Lenz's Law).
3. Deceleration:
  - The opposing magnetic field creates a force that acts upward on the falling magnet, causing it to decelerate.
  - The speed of the magnet decreases as it passes through the region where the magnetic flux is changing most rapidly.
4. Passing Through the Ring:
  - As the magnet moves through the ring and starts to exit the other side, the rate of change of the magnetic flux decreases, reducing the induced current and the opposing magnetic force.
  - The magnet starts to accelerate again, but this time the acceleration is less than the initial acceleration due to gravity because the opposing force is still present but diminishing.
5. After Passing Through the Ring:
  - Once the magnet is far enough below the ring, the induced currents and the opposing magnetic forces become negligible.
  - The magnet resumes accelerating under gravity alone, but its speed is lower than it would have been if it had fallen without the ring.
Graphical Representation:
- Option A:
 - The graph shows an initial increase in speed as the magnet accelerates due to gravity.
 - Then, there is a decrease in speed as the magnet decelerates due to the opposing magnetic force induced by the ring.
 - After passing through the ring, the speed increases again, but the curve is less steep than the initial acceleration, indicating a lower overall speed compared to free fall without the ring.
Conclusion:
Option A correctly represents the speed vs. time graph of the bar magnet as it falls through the center of the conducting ring, showing the initial acceleration, subsequent deceleration, and the final increase in speed after passing through the ring. This is why option A is the correct answer.
So The correct answer is option (A):