Question

A magnet is dropped into an infinitely long vertical copper tube. Then

• A. The magnet moves with continuously decreasing velocity and ultimately comes to rest
• B. The magnet moves with continuosly increasing velocity and ultimately acquires a constant terminal velocity
• C. The magnet moves with constant velocity.
• D. The magnet moves with continuously increasing velocity but constant acceleration.

Answer 1

The correct option is B The magnet moves with continuosly increasing velocity and ultimately acquires a constant terminal velocity

When the magnet is dropped down through an infinitely long copper tube, the magnetic flux, linked with different cross-sections of copper tube, changes continuously.

Due to this change in flux linked with the copper tube, there is induction of current inside the copper tube.

According to the Lenz’s law, the current induced opposes the change in the magnetic field linked with the copper tube and hence, applies an upward force on the magnet.

The other force acting on the magnet is its own weight in the downward direction.

Since, initially the magnet is under free fall and moves under the influence of the acceleration due to gravity, the velocity of the magnet increases in the downward direction, or the net acceleration of magnet is downwards.

But as the magnet moves downward with increasing velocity, the induced current increases in magnitude (due to increase in the magnitude of induced emf).

Hence, the retarding force by the induced currents increases to such an extent, that at a point the weight of the magnet in downward direction becomes equal to the upward retarding force.

At this situation, the velocity of the magnet becomes constant for the rest of the journey of the magnet. This constant velocity is called terminal velocity. When the magnet attains terminal velocity, its acceleration becomes zero and remains zero thereafter.

Therefore, when the magnet is dropped vertically down in a copper tube, the magnet moves with continuously increasing velocity and ultimately acquires a constant terminal velocity.

Hence, option $\left(B\right)$ is the correct answer.