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Is this analogy of Induced emf correct?

Physics Asked on December 6, 2020

I have searched PSE (and many other sites on internet) for the theoretical reason of induced emf. All I got was that the phenomenon of Induced EMF is experimental fact and can only be mathematically understood using Maxwell’s equations.

For the last few days I have thinking about it and I found an analogy and would like some experienced physicists to find the flaw in the analogy.

Now to begin with, Lets imagine you are on a train (facing the same direction in which the train is moving). Say about 100 metres away , you see a circular tunnel in the path of the train. The train is moving towards the tunnel. What would you expect to see?

Well , from your perspective, you would see that as time passes , the tunnel appears to get bigger and bigger for you.

Now here comes the fun part. Replace the tunnel with a conducting loop and train with a magnet. The question is what would the magnet see ?

The magnet will see that the loop is getting bigger and bigger with time.

OR

It will see that the circumference of the loop is going perpendicularly away from it. And what happens when some conductor moves perpendicularly to a magnetic field?. Emf is induced in it (a.k.a motional emf ; which can be understood theoritically).

Lets take a quick example:

  1. You are the magnet and the North pole to facing towards the coil
  2. This means Magnetic field lines are coming out from the front.
  3. As you are taken near to the conducting loop, you will see that the electrons in the circumference of the loop is getting away from you perpendicularly.
  4. You will apply some force F = $-vec{v}×vec{B}$ on the electrons. The electrons will thus move in a clockwise manner. Meaning that the current will flow anticlockwise.
  5. And thus you have successfully induced the emf that opposes your motion.

I know this type of question is off topic on PSE but I just want some theoretical explanation of the phenomenon from some experienced physicists and also to point out if there is something wrong in this analogy.

One Answer

The loop represented by the tunnel is apparently getting bigger as viewed from the train or magnet as it approaches. It is not actually getting bigger - this means that the charges in the loop do not feel a Lorentz force - in the way you describe- and therefore there is no induced current in this loop from this cause you describe. The reason why a changing magnetic field causes an EMF induced in a conductor (such that the current acts in a direction which creates a magnetic field opposing the original one) is due to conservation of energy. This should also have been in the books you read to study induced currents.

Answered by Dr jh on December 6, 2020

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