Electricity & Megnetism

# Lenz’s Law of electromagnetic induction

## What is Lenz’s Law of electromagnetic induction?

Lenz’s law states that:”The direction of induced current is always so as to oppose the change which causes the current.”
A mathematical expression of Faraday’s law of electromagnetic induction was derived as:

ε = – N ΔΦ/Δt

The minus sign in the expression is very important. It has to do with the direction of the induced emf. To determine the direction we use a method based on the discovery made by the Russian Physicist Heinrich Lenz in 1834. He found that the polarity of an induced emf always leads to an induced current that opposes, through the magnetic field of the induced current, the change-inducing the emf. This rule is known as Lenz’s law.
Lenz’s law refers to induced currents and not to induced emf, which means that we can apply it directly to closed conducting loops or coils. However, if the loop is not closed we can imagine as it were closed, and then from the direction of the induced current, we can find the direction of the induced emf.
Let us apply the Lenz’s law to the coil in which current is induced by the movement of a bar magnet. We know that a current-carrying coil produces a magnetic field similar to that of a bar magnet. One face of the coil acts as the north pole while the other one as the south pole. If the coil is to oppose the motion of the bar magnet, the face of the coil towards the magnet must become a north pole as shown in fig below. A bar magnet moves toward a stationary metal loop, as in figure(a). As the magnet moves to the right toward the loop, the external magnetic flux through the loop increases with time. As a result, the induced current set up in the loop which produces magnetic field, as illustrated in figure (b). Knowing that like magnetic poles repel each other, we conclude that the left face of the current loop acts as a north pole and that the right face acts as a south pole.
If the magnet moves to the left, as in figure (c), its flux through the area enclosed by the loop decreases in time. Now the induced current in the loop produces the magnetic field as shown in figure (d).In this case, the left of the loop is a south pole and the right face is a north pole.

### Lenz’s Law  and Conservation of Energy

“Lenz law is the statement of law of conservation of energy for the circuit involving induced current”

To understand this statement, consider a conducting bar moving tot he right on two parallel rails in the presence of a uniform magnetic field as shown in the figure below. As the bar moves to the right, the magnetic flux through the area enclosed by the circuit increases with time because of the area increases. As a result, the induced current must be directed counterclockwise when the bar moves to the right. Since the current-carrying bar is moving in the magnetic field, it will experience a magnetic force FB. By using the right-hand rule, the direction of   FB is opposite to that of v, which tends to stop the rods. An external dragging force must be applied to keep the rod moving in the magnetic field.
The dragging force provided the energy for the induced currents flow. This energy is the source of induced current. Thus the electromagnetic induction is exactly according to the law of conservation of energy. If the bar is moving to the left, as in figure (b), the external magnetic flux through the area enclosed by the loop decreases with time.Because the field is directed into the page, the direction of the induced current must be clockwise.
Lenz’s law of electromagnetic induction (video)

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