When a bar magnet falls through a long hollow metal cylinder fixed with its axis vertical, the final acceleration of the magnet is

Options

A. Equal to zero
B. Less than g
C. Equal to g
D. Equal to g in to beginning and then more than g

Answer

To solve the problem of a bar magnet falling through a long hollow metal cylinder, we can break it down into a series of steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a bar magnet that is falling through a long hollow metal cylinder. The cylinder is fixed vertically, and the magnet is initially at rest.

2. **Initial Condition**:
- When the bar magnet is released, it starts falling under the influence of gravity. Initially, the magnet has zero velocity.

3. **Induction of EMF**:
- As the magnet falls, it moves through the magnetic field created by its own magnetic poles. This motion changes the magnetic flux through the hollow cylinder, which induces an electromotive force (EMF) in the cylinder according to Faraday's law of electromagnetic induction.

4. **Induced Current**:
- The induced EMF causes a current to flow in the metal cylinder. According to Lenz's law, this induced current will flow in such a direction that it opposes the change in magnetic flux that produced it. This means the induced current will create a magnetic field that opposes the motion of the falling magnet.

5. **Net Force on the Magnet**:
- The falling magnet experiences two forces: the gravitational force acting downward (mg) and the upward magnetic force due to the induced current in the cylinder. Initially, the gravitational force is greater than the induced force, so the magnet accelerates downward.

6. **Terminal Velocity**:
- As the magnet continues to fall, the induced current increases, which increases the opposing magnetic force. Eventually, the upward magnetic force will equal the downward gravitational force (mg). At this point, the net force on the magnet becomes zero.

7. **Final Acceleration**:
- When the net force is zero, the acceleration of the magnet also becomes zero. This means that the magnet will continue to fall at a constant velocity known as terminal velocity.

8. **Conclusion**:
- Therefore, the final acceleration of the magnet as it falls through the long hollow metal cylinder is **zero**.

### Final Answer:
The final acceleration of the magnet is **0 m/s²**.

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