Question

A magnet is dropped down an infinitely long vertical copper tube
A. The magnet moves with continuously increasing velocity and ultimately acquires a constant terminal velocity
B. The magnet moves with continuously decreasing velocity and ultimately comes to rest
C. The magnet moves with continuously increasing velocity but constant acceleration
D. The magnet moves with continuously increasing velocity and acceleration

Answer 1

Hint: Recall the concept of change in magnetic flux and generation of eddy current due to the motion of the bar magnet. Also use the concept of Lenz’s law. Hence, check the force acting on the magnet moving in the downward direction when it is moving down in an infinitely long copper tube. Hence, check the effect of the eddy current on the velocity of the magnet.

Complete answer:
When the magnet is dropped down through an infinitely long copper tube, the magnetic flux linked with the copper tube changes continuously. Due to this change in flux linked with the copper tube, there is induction of an eddy current.According to the Lenz’s law, the eddy current generated opposes the change in the magnetic field linked with the copper tube and hence, applies an upward retardation force on the magnet.The other force acting on the magnet is its own weight in the downward direction.

Since the magnet is in the free fall and moves under the influence of the acceleration due to gravity, the velocity of the magnet increases in the downward direction and the magnet is in the acceleration motion (that is the magnet has an acceleration in the downward direction).But as the magnet moves downward with increasing velocity, the eddy current generated oppose the change in magnetic flux linked with the copper tube largely. Hence, the retarding force by the eddy currents increases to such an extent that at a point the weight of the magnet in downward becomes equal to the upward retarding force.

At this situation, the velocity of the magnet becomes equal to the terminal velocity and this terminal velocity remains the same for the whole journey of the magnet.This constant velocity of the magnet leads in zero acceleration of the magnet.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, the correct option is A.

Note: The students should keep in mind that there is change in magnetic flux linked with the copper tube because we have considered the magnetic field due to the magnet in motion is non-uniform. Also the students should keep in mind that the gravitational force has an influence on the motion of the magnet.