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Ishaan
Ishaan
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A bar magnet is released under gravity inside a long copper tube along the axis of the tube.

The answer is given that(edit :) it will stopmoves with constant velocity. But I don't understand how.

My research :

The bar magnet is falling with an acceleration of $g$. So its speed increases. Thus the flux change also increases with time. And thus ultimately, the induced emf also changes as induced emf is directly proportional to the change of magnetic flux through the loop (the copper tube consists of infinite copper loops).

Now according to Lenz's Law, the induced emf produces a magnetic flux as to oppose the change in the magnetic flux through the loop. Consider, the magnet to fall vertically downward, thus a magnetic flux is induced vertically upwards. Thus a vertical force is applied to the magnet in the upwards direction.

What I do not understand is that won't the 'induced' force oppose the acceleration due to gravity. And if it opposes, the velocity of the magnet becomes less, thus the emf and ultimately the induced force becomes less. And the gravitational force dominates again. Will the motion be oscillatory, or will it stop? If it will stop, can you provide an elaborated reason? Thank You!

A bar magnet is released under gravity inside a long copper tube along the axis of the tube.

The answer is given that it will stop. But I don't understand how.

My research :

The bar magnet is falling with an acceleration of $g$. So its speed increases. Thus the flux change also increases with time. And thus ultimately, the induced emf also changes as induced emf is directly proportional to the change of magnetic flux through the loop (the copper tube consists of infinite copper loops).

Now according to Lenz's Law, the induced emf produces a magnetic flux as to oppose the change in the magnetic flux through the loop. Consider, the magnet to fall vertically downward, thus a magnetic flux is induced vertically upwards. Thus a vertical force is applied to the magnet in the upwards direction.

What I do not understand is that won't the 'induced' force oppose the acceleration due to gravity. And if it opposes, the velocity of the magnet becomes less, thus the emf and ultimately the induced force becomes less. And the gravitational force dominates again. Will the motion be oscillatory, or will it stop? If it will stop, can you provide an elaborated reason? Thank You!

A bar magnet is released under gravity inside a long copper tube along the axis of the tube.

The answer is given (edit :) it moves with constant velocity. But I don't understand how.

My research :

The bar magnet is falling with an acceleration of $g$. So its speed increases. Thus the flux change also increases with time. And thus ultimately, the induced emf also changes as induced emf is directly proportional to the change of magnetic flux through the loop (the copper tube consists of infinite copper loops).

Now according to Lenz's Law, the induced emf produces a magnetic flux as to oppose the change in the magnetic flux through the loop. Consider, the magnet to fall vertically downward, thus a magnetic flux is induced vertically upwards. Thus a vertical force is applied to the magnet in the upwards direction.

What I do not understand is that won't the 'induced' force oppose the acceleration due to gravity. And if it opposes, the velocity of the magnet becomes less, thus the emf and ultimately the induced force becomes less. And the gravitational force dominates again. Will the motion be oscillatory, or will it stop? If it will stop, can you provide an elaborated reason? Thank You!

Source Link
Ishaan
Ishaan
  • 105
  • 1
  • 7

The fate of a bar magnet released in an infinitely long copper tube

A bar magnet is released under gravity inside a long copper tube along the axis of the tube.

The answer is given that it will stop. But I don't understand how.

My research :

The bar magnet is falling with an acceleration of $g$. So its speed increases. Thus the flux change also increases with time. And thus ultimately, the induced emf also changes as induced emf is directly proportional to the change of magnetic flux through the loop (the copper tube consists of infinite copper loops).

Now according to Lenz's Law, the induced emf produces a magnetic flux as to oppose the change in the magnetic flux through the loop. Consider, the magnet to fall vertically downward, thus a magnetic flux is induced vertically upwards. Thus a vertical force is applied to the magnet in the upwards direction.

What I do not understand is that won't the 'induced' force oppose the acceleration due to gravity. And if it opposes, the velocity of the magnet becomes less, thus the emf and ultimately the induced force becomes less. And the gravitational force dominates again. Will the motion be oscillatory, or will it stop? If it will stop, can you provide an elaborated reason? Thank You!