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My book states that:

  • In Lenz's Law, mechanical energy of the magnet gets converted to electrical energy, hence Law of Conservation of Energy is maintained.

  • But Faraday's Law tells that if relative velocity of magnet with respect to conductor is constant, the induced EMF as well as current is constant as well(It is what is written in my book as an interpretation of Faraday's Law, and my interpretation of it according to what I have learnt from my book too)

But aren't the two statements contradicting each other? Since if I move a magnet closer to the conducting coil making sure that I adjust the force applied on it accordingly so that constant velocity is maintained, I am constantly doing work on it, which means in absence of the conducting coil, its kinetic energy would have kept increasing. Now that it is not, shouldn't the current not be constant? As that means part of my energy is being lost as I am constantly losing energy.

Or do I have to consider it that a constant current also produces a constantly increasing electrical energy with time since it is equal to $Vit$?

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    $\begingroup$ if relative velocity of magnet with respect to conductor is constant, the induced EMF as well as current is constant as well Please give an example. $\endgroup$
    – Farcher
    Commented Mar 5, 2022 at 8:23
  • $\begingroup$ @Farcher I do not have examples, it is what is written in my book as an interpretation of Faraday's Law(and my interpretation too) $\endgroup$ Commented Mar 5, 2022 at 8:25
  • $\begingroup$ Textbook or your notes? The reason I ask is that I am not so sure that it is a correct statement. $\endgroup$
    – Farcher
    Commented Mar 5, 2022 at 9:29
  • $\begingroup$ @Farcher textbook $\endgroup$ Commented Mar 5, 2022 at 14:20
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    $\begingroup$ You should probably include more context and maybe mention which textbook you are talking about. The second statement for example isn't always valid. $\endgroup$
    – Puk
    Commented Mar 7, 2022 at 20:00

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In this example the coil and the magnet are oriented so that gravity isn't influencing the movement of the magnet. These laws work in conjunction with each other. Lenz's law is correct and that induced electrical energy creates a current in the coil of wire. This current in the wire will create an opposing magnetic field resisting the movement of the magnet. This opposing force will increase with the velocity of the magnet. As long as the force that is causing the magnet to move doesn't change there will be a velocity of the magnet that causes the forces acting on the magnet to reach an equilibrium.

You are correct about the work that is being done on the magnet from you pushing on it but there is also another opposing force from the coil that needs to be taken into account.

A way to think about this is like an object falling due to gravity and reaching terminal velocity. Since the force from the air resistance is now equal to the force of gravity. Gravity is the force being applied to the magnet and the air resistance is the opposing force from the coil of wire.

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