Lenz's Law, Significance, Applications & Formula

An efficient method of generating electricity is known as electromagnetic induction. From electricity generation to distribution, they are used everywhere. This is a procedure in which an electric voltage or electromotive force is generated through a conductor by changing magnetic flux or magnetic fields. This theory of electromagnetic induction was based on Faraday's laws and Lenz's law discovered by Michael Faraday in 1830.

The generation of electromagnetic induction can be achieved through two methods where in the first method there is an electrical conductor within a moving magnetic field and in the second method the electrical conductor moves steadily in a stationary magnetic field. Therefore, this article covers an overview of Lenz's law with examples.

What is Lenz's law?

The name Lenz's Law was taken from the physicist Emil Lenz when he invented this law in 1834. Lenz's Law states this; The direction of the induced current flowing in a conductor through a changing magnetic field and then the magnetic field formed through the induced current will resist the early changing magnetic field.

Once a current is induced through a magnetic field, the magnetic field generated by the induced current will form its magnetic field. Therefore, this field will be restricted by the magnetic field that formed it.

Lenz's law

Lenz's law is mainly based on Faraday's law of electromagnetic induction because Faraday's law states that a changing magnetic field will induce the flow of current within an electrical conductor while Lenz's law states that the direction of the induced current constrains the early changing magnetic field that generated it. Thus, this is indicated in the formula for Faraday's law by the negative sign.

ϵ = −dΦB / dt

The magnetic field can be adjusted by changing the strength of its field or by moving the magnet in the direction of the coil or away from the coil, etc. Thus, we can say that the magnitude of the induced electromagnetic field inside the circuit is proportional to the change in flow rate.

ε ∝ dΦ / dt

Lenz's Law Formula

According to Faraday's law, when an emf is produced by a change within the magnetic flux, it is known as Lenz's law. Here, an induced current can be generated through the polarity of the induced EMF as the magnetic field constrains the changing primary magnetic field. In Faraday's law of electromagnetic induction, the negative sign mainly determines the induced EMF or ε and the change within the magnetic flux or B has opposite signs. Here, the formula for Lenz's law is given below:

Lenz's Law Formula Emf = -N (ΔΦ / Δt)

where:

"Emf" = induced potential or electromotive force.

"N" = number of loops.

“Δϕ” = Change within the magnetic flux.

"Δt" = change in time.

Lenz's Law and Conservation of Energy

The direction of the induced current by Lenz's law must generate a magnetic field to comply with the energy conservation that restricts the magnetic field it produced. This law is a consequence of the law of conservation of energy.

Once the magnetic field is formed by the induced current it will be in the same direction as the field generated by it, then these magnetic fields will merge to form a larger magnetic field.

This magnetic field will cause one additional current in the conductor to double the size of the induced current. Thus, we can conclude that if Lenz's law does not state that the induced current must form a magnetic field to constrain the resulting field, we will end up with a positive non-stop feedback loop to break the power protection.

This law is generally governed by Newton's third law of motion, which states that for every action there is an equivalent and opposite reaction. If the induced current forms a magnetic field equivalent and opposite to the direction of the magnetic field it makes, then it only resists the change of magnetic field within the region.

Experiment

This Lenz's Law experiment is basically to find out which direction of induced electromotive force and current we are looking for is Lenz's Law. For this law, the following three experiments are proven by his theory.

Lenz's Law Experiment

The first experiment

In this experiment, Emil Linz said that when current flows inside a circuit coil then it generates magnetic field lines. When the current supply inside the coil increases, the magnetic flux will increase. Therefore, the direction of the induced current flow will be restricted once it enhances the magnetic flux.

second experience

In this second experiment, Lenz declared that once the current-carrying coil is hit over an iron rod with its left terminal acting like the N electrode and oriented towards the coil “S”, then an induced current will be generated.

The third experience

In this third experiment, Lenz stated that as soon as the coil is pulled in the direction of the magnetic flux, the coil attached to it decreases. Therefore, based on Lenz's law, the movement of the coil is restricted once the induced current is supplied in a similar direction.

To generate an induced current, the magnetic field uses a force on the coil, and sequentially, a force through the current supply in the magnetic field is used to constrain it.

Lenz law problems and solutions

1). Round shaped wire coil includes 350 turns and a radius of 7.5 cm horizontally over a table. The coherent magnetic field mode is turned open progressively, so the magnetic field strength can be expressed as a time function as B(t) = 0.02 (T/s2) × t2. So, what is the full EMF within the file as the time function, and in what way does the current rendering?

EMF = (-N) x (22/7 x r^2) x (d/dt B)

= -350 x 22/7 x (0.075 m)^2 x 2 x 0.020 tons x tons

= -25 tons * (Tm^2 / s^2)

= -25 volts/sec

Clockwise is provided.

2). If the current flow inside the wire is from direction B to A, find out the direction of current induced inside the metal ring wire left aside as shown in the following figure.

current flowing in a wire

Based on Lenz's law, the induced current will limit the cause of its production. Thus, current flowing inside a loop will induce support current flowing inside the wire which means in a similar direction. As a result, the current direction inside the loop will be clockwise.

3). In a circular loop, resistance R and area A rotates with angular velocity ω on an axis throughout its diameter shown below. The ring plane is essentially perpendicular to a stable magnetic field B. Please find the induced current inside the circuit loop.

uniform magnetic field

The direct magnetic flux throughout the loop is

ΦB = BA cos θ

Here, θ = ωt, and therefore, ΦB = BA cos t

According to Faraday's law,

ϵ = −dΦB / dt = - ϵ = −d / dt [BA cosωt]

ϵ = [BAω sinωt]

The induced current can be expressed as

I = E / R = (BAω / R) sinωt

Here, both the current and the induced emf change sinusoidally. So, the emf amplitude is “BAω” and the current is BAω/R.

Lenz's Law Advantages

The significance of Lenz's law includes the following.

Lenz's Law tells us two main things about how a changing magnetic field interacts with a conductor loop.

This law is based on the conservation of energy but not on the conservation of momentum

This law is available to judge how magnetic fields are generated by conductors carrying alternating current or direct current.

This law states the direction of the induced current to the rate of change within the induced magnetic field.

In electromagnetism, this law is a very important concept

Limitations of Lenz's Law

The limitations of Lenz's law include the following.

Once the magnet is moved in the direction of the coil, the external magnetic field will induce a current inside the coil to make its internal magnetic field through the same magnitude but with the opposite direction, thus opposing the change.

Once the magnet moves through the coil or any other face of the coil, the flow of current will change direction and the internal magnetic field will be strengthened in a similar direction due to the external magnetic field, so again opposing the change.

Where is Lenz's Law used/applications?

Applications of Lenz's law include the following.

This law is very useful in understanding the concept of magnetic energy stored inside an inductor

When an emf source is connected through an inductor, current begins to flow through it, and the reverse emf will limit the increasing flow of current through the inductor. To create the current flow, an external emf source has to do some work to overcome this opposition. So this work can be done by the emf stored inside the inductor and can be improved by simply disconnecting the external source of the emf from the circuit.

Lenz's law specifies that the induced emf and the change within the flow have inverse signs that give a physical understanding of the alternative.

Lenz's Law, Significance, Applications & Formula