JEE MainPhysicsMagnetic Properties of Matter
A small bar magnet is released from rest and falls under gravity through a very long vertical copper tube. Which of the following best describes the variation of the magnet's velocity ( v ) with time ( t ) as it falls through the tube?
Options
- AA curve starting from the origin, whose slope continuously decreases to zero as the velocity approaches a cons
- BA straight line passing through the origin with a constant positive slope, representing free fall acceleration
- CA curve starting from the origin, reaching a maximum value, and then decreasing to zero as the magnet stops in
- DA curve starting from the origin, whose slope continuously increases with time due to the combined effect of g
Correct answer
A. A curve starting from the origin, whose slope continuously decreases to zero as the velocity approaches a cons
Step-by-step solution
When the magnet falls, the changing magnetic flux induces eddy currents in the copper tube. According to Lenz's law, these induced currents produce a magnetic force that opposes the downward motion of the magnet. The magnitude of this opposing force is proportional to the velocity of the magnet ( F_ m = kv ). The net downward force on the magnet is F_ net = mg - kv , which means the acceleration is a = g - k m v . As the velocity v increases, the downward acceleration a (which is the slope of the v-t graph) decreas