Question

A small bar magnet is dropped through different hollow copper tubes with same length and inner diameter but with different outer diameter. The variation in the time (t) taken for the magnet to reach the bottom of the tube depends on its wall thickness (d) as

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is C

To solve this question, we need to understand the physics behind the problem. When a bar magnet is dropped through a conductive non-magnetic hollow tube, like a copper tube, it induces eddy currents in the walls of the tube. These eddy currents, in turn, produce a magnetic field that opposes the motion of the magnet due to Lenz's law, which states that the direction of induced current will be such that it will oppose the change that caused it.

The amount of eddy current induced is directly related to the thickness of the tube walls, denoted by d. As the thickness increases, the resistance to the flow of eddy currents decreases, which means that more current is generated for the same rate of change of magnetic flux.

In terms of the graph options provided, the time t that the magnet takes to reach the bottom of the tube is affected by these eddy currents. Greater wall thickness leads to greater eddy current production, which effectively increases the time due to increased opposing forces acting on the magnet.

Thus, a thicker wall induces larger eddy currents and hence more magnetic damping, slowing the magnet down more significantly. Therefore, the relationship between time t and wall thickness d should show an increasing trend.

The correct graph should depict this relationship as increasing. Thus, among the provided options, the correct answer is the graph that shows time t increasing with wall thickness d:

This graph clearly demonstrates that as the wall thickness increases, so does the time taken by the magnet to reach the end of the tube, which is consistent with our analysis based on Lenz's law and eddy current phenomena.