Magnetic pendulum and electric energy....

[KedarMhaswade]

TL;DR Summary

A simple pendulum oscillating inside a coil obviously does not generate electricity, or does it?

While reading about electromagnetism from the OpenStax books with my son (and doing some experiments), he asked this question.

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Suppose I hang a pendulum and make it oscillate inside a coil connected to a Galvanometer as shown in the schematic diagram:

Hopefully the image is clear enough. His argument is that the analysis of the pendulum from Newtonian mechanics suggests that the initial potential energy that I provide to it ($mgh$) is converted into its kinetic energy ($\frac{1}{2} mv^2$). Then the energy dissipates through losses as pendulum eventually comes to a standstill. Thus, the energy I provide in raising the magnet initially is finally lost in friction or to the surrounding air.

But if the magnet is made to oscillate inside a coil, according to Faraday's law, electricity is generated in the coil as the Galvanometer needle shows the deflection. The pendulum does not know that it is made to oscillate inside a coil and it ends up inducing electromotive force in it (as a mere side-effect).

Have I not generated electrical energy violating the law of conservation of energy?

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How will you refute this claim?

Does Lenz's law come into the picture and slow down the magnet (since $F = -\frac{d\phi}{dt}$) which would not have happened had the magnet pendulum not oscillated inside the coil?

 

[kuruman]

Summary:: A simple pendulum oscillating inside a coil obviously does not generate electricity, or does it?

Does Lenz's law come into the picture and slow down the magnet (since F=−dϕdt) which would not have happened had the magnet pendulum not oscillated inside the coil?

Absolutely. The induced current in the coil generates heat because the coil has non-zero resistance. That's where the energy goes. The magnet will execute damped harmonic motion and come to a stop regardless of air resistance. You may wish to read about eddy current braking here.

 

[Dale]

The pendulum does not know that it is made to oscillate inside a coil

Putting something in bold doesn't make it true. There is a force exerted on the pendulum with the coil that does not exist without the coil. So in the sense that the pendulum "knows" anything it does know that it is made to oscillate inside a coil.

Have I not generated electrical energy violating the law of conservation of energy?

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How will you refute this claim?

By pointing out the recognized fact that it violates the conservation of energy so it must be wrong.

 

[KedarMhaswade]

Putting something in bold doesn't make it true.

True ;-). Wouldn't the button say "True" otherwise?