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How does Lenz Law relate to the law of conservation of energy?

July 16, 2021, Physics

Did you know that the Lenz law is also referred to as the law of conservation of energy? Can you relate one to the other? Let’s look at how these two laws relate to each other.

To understand this, first, let’s recall Faraday’s law of electromagnetic induction. It states that whenever there is a change in the magnetic flux associated with the coil or conductor, EMF is induced in that conductor. The change in flux may be due to the increase or decrease in the flux or movement of the coil or conductor in the magnetic field. The mathematical expression for Lenz law is,

\[ EMF= -N \frac{d \phi}{dt} \]

N stands for the number of turns in the coil, and ​\( \phi \)represents the flux associated with the coil.

Lenz’s law explains the negative sign in the equation for Faraday’s law.

Lenz law states that the direction of the induced EMF is such that it opposes the cause that induces an EMF. If EMF is induced due to an increase in the flux, induced EMF will produce the flux in the opposite direction to the original flux. If induced EMF is due to a decrease in flux, the EMF will produce the flux in the same direction so that it opposes the decrease in flux. If EMF is induced due to the motion of a conductor in the magnetic field, the induced EMF will oppose the motion itself.

Let’s discuss Lenz’s law with an interesting example. 

Assume an ideal situation where the coil is rotating in the magnetic field. There is no friction, no force opposing the rotation of the coil in the field. From Newton’s first law of motion, the coil will continue its motion unless it is acted upon by an external force.

As per Faraday’s law, the EMF will be induced in the coil. Because it passes through the magnetic field and cuts the flux associated with it.

So now, if there is no external force acting on the coil, it will continue to rotate and produce an EMF, which is also a form of energy, out of nowhere. This will violate the law of conservation of energy as energy can neither be created nor be destroyed.

Lenz’s law states that the current due to induced EMF will flow in such a way that it produces a magnetic field and force which will oppose the motion of a conductor in the magnetic field.

It simply means, to keep the coil rotating in the field, you will have to keep on applying the force on it. That implies that you need to keep on supplying the mechanical energy to the coil, which will be converted into electrical energy. And that’s how electricity is produced.


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