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Question

A bar magnet is released from rest along the axis of a very long, vertical aluminum tube. After some time the magnet:


A

will stop in the tube

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B

will move with an acceleration g

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C

will move with almost constant speed

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D

will oscillate

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Solution

The correct option is C

will move with almost constant speed


Electromagnetic Induction

  1. Magnetic flux is defined as the density of magnetic field lines passing through a given area.
  2. It gives us the strength of the magnetic field in that given area.
  3. Faraday showed experimentally that whenever the magnetic flux linked with a closed circuit changes with time an electric current is induced in the circuit.
  4. This phenomenon is known as electromagnetic induction.
  5. According to Faraday's law of electromagnetic induction, the induced emf in a circuit is proportional to the rate of change of magnetic flux linked with the circuit.
  6. According to Lenz's law of electromagnetic induction, the direction of induced emf is such that it tries to oppose the cause of its generation, ie, the variation of magnetic flux producing it.

Motion of the Magnet

  1. When the bar magnet is initially dropped, it will fall with an initial acceleration due to gravity g.
  2. Now we know that when a magnet moves, there will be a change in flux.
  3. Again, due to the change in flux, a current will be induced on the aluminum tube.
  4. The induced current will be such that it will oppose the magnetic field.
  5. So an opposing force will be applied to the bar magnet till the time, the magnetic flux keeps changing.
  6. The magnetic flux will keep changing until the net force applied to the magnet is zero, or the magnet is no longer under acceleration.
  7. As a result, the current through the aluminum tube keeps changing, and hence an opposing magnetic field will be induced.
  8. The magnitude of the opposing magnetic field will also increase with an increase in changing magnetic flux.
  9. Ultimately there will come a point where the force from the opposing magnetic field is equal to the weight of the magnet.
  10. In that case, the acceleration acting on the magnet as well as the change in magnetic flux will become zero.
  11. As a result, the opposite magnetic field will not change anymore.
  12. In the meantime, when the net force on the magnet is zero, the magnet will acquire a velocity.
  13. Therefore, after some time the magnet will move with almost constant speed.

Hence, the correct answer is option (C).


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