#Month of Equations: What does the Lenz’s law really mean?

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Meaning of the Equation:

Lenz’s law states that the current induced in a current carrying loop by changing the magnetic flux is such that the magnetic field produced by the induced current opposes the change in magnetic field.

A law that draws attention towards the most fascinating property of nature. This equation simply means that a change in magnetic flux through a current carrying loop generates an emf that gives rise to the induced current in the loop. However, the negative sign on the right-hand side of this equation has a different story to tell. The negative sign indicates that the emf or the induced current would be in a direction such that it opposes the change in magnetic flux through it. Let us try to understand this principle from scratch as always :

In the 1830’s, the principle of electromagnetic induction was discovered by Michael Faraday. It states that a relative motion between a magnetic and conducting loop gives rise to an e.m.f or induced current in the loop. Lenz’s law marks an important property of this induced current by identifying the direction in which this induced current flows. I will explain what this means by a simple example:

Case -I: Consider that you move a bar magnetic towards a conducting loop while pointing the north pole of the magnetic towards the loop. This will change (increase) the amount of flux crossing the conductor and thus give rise to an induced current. Now, Lenz’ law states that the direction of current produced will such that by the clock-rule, the front conducting surface (facing north-pole of the magnet) would become a magnetic north pole and repel the magnet coming towards it and hence, try to decrease the flux.

Case-II: Now imagine that you placed the magnet initially close to the loop with its north pole facing the loop as before and then you begin taking the magnet away from the conducting loop. In this case, the induced current will be in a direction opposite to the previous case such that the conductor’s end facing the magnet would be a magnetic south pole. This will lead to the conductor attracting the magnet towards itself and trying to increase the magnetic flux through it. Pretty strange! This behavior was put into simple words by D. J. Griffiths as:

Nature abhors a change in flux.

Another remarkable property of today’s equation is that it obeys the principle of conservation of energy. One may be intrigued as How?

Consider it this way, due to the induction of a magnetic north pole in the first case, now if we still have to move the magnet towards the conductor, we have to do some work against the force of repulsion between the magnetic north pole induced in the conductor and the north pole of the magnet. This work done will be converted into heat energy that is normally produced in an inductor. Even in the second case, we have to do some work against the attractive forces between the south pole of the conducting loop and the north pole of the bar magnet to pull the bar magnet away, this work would show up in the form of heat. Hence, if there would have been no repulsion (attraction) in the first (second) case, the conductor would simply attract (repel) the magnet moving towards (away) from it and the law of conservation of energy would be violated as we could not have known the source of the heat generated during this process.

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