[Physics] A paradox to Lenz’s law

conservation-lawselectromagnetismenergy-conservation

I have read that in simple words, Lenz's law states that:

The direction of current induced in a conductor is in such a fashion, that it opposes its cause.

This validates law of conservation of mass-energy.

I arranged the following thought experiment:

Let there be a pendulum with its bob being a small bar magnet. The pendulum is oscillating in a direction parallel to the horizontal axis of the bar magnet on which the North and South poles lie. Also, the pendulum is in complete vacuum. (But gravity is there to make the pendulum oscillate.)

At one of the extreme positions of the pendulum, we keep a solenoid, ends of which are connected to a load resistance.

As the North pole of the bar magnet approaches the solenoid, current is induced in the solenoid in such a fashion that a North pole is formed at the end near to the bar magnet's North pole, and the bar magnet gets repelled towards the other side.

The bar magnet then goes to the other end and then comes back (as a pendulum does) and again the same process is repeated. This should go on forever, and current should keep appearing across the load resistance.

How does the law of conservation of energy hold here?

Best Answer

As the magnet approaches the solenoid, a current is induced. The current generates a magnetic field. The field repels the magnet, slowing it's approach. The amplitude of the oscillations diminish.

If there was no resistance, this would work in reverse as the magnet receded from the solenoid. The magnetic field would accelerate the magnet. The magnet would induce a current in the other direction, reducing the current to 0. This would reduce the field of the solenoid to 0. The amplitude would not diminish.

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