# What is Lenz’s Law : Formula, Significance & Its Applications

An efficient method for generating electricity is known as electromagnetic induction. From electricity generation to distribution, it is used everywhere. This is a procedure where a Voltage or electromotive force is generated across a conductor through changing Magnetic Flux or Magnetic Fields. This electromagnetic induction theory was based on Faraday’s laws & **Lenz’s law** which were discovered in the year 1830 by Michael Faraday.

The Electromagnetic Induction generation can be achieved through two methods where in the first method an electrical conductor is located within a moving magnetic field and in the second method the electrical conductor is moving steadily in a fixed magnetic field. So, this article discusses an overview of Lenz’s Law with its examples.

## What is Lenz’s Law?

The name Lenz’s Law was taken from the physicist Emil Lenz when he invented this law in the year 1834. Lenz’s law states that; the flow of current direction which is induced in a conductor through a varying magnetic field 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, then the magnetic field generated through the induced current will form its magnetic field. So, this field will be restricted through the magnetic field that formed it.

Lenz’s law mainly depends on Faraday’s law of electromagnetic Induction because Faraday’s law states that a varying magnetic field will induce a flow of current within an electric conductor while Lenz’s law states that the induced current direction which restricts the early changing magnetic field which generated it. Thus, this is denoted in Faraday’s law formula through the negative sign.

**ϵ = −dΦB/dt**

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

**ε ∝ dΦ/dt**

### Lenz’s Law Formula

According to Faraday’s Law, when an emf is produced through a change within magnetic flux is known as Lenz’s law. Here, an induced current can be generated through the induced EMF’s polarity where the magnetic field restricts the primary changing magnetic field. In Faraday’s law of electromagnetic induction, the negative sign mainly specifies the induced EMF or ε & the change within magnetic flux or δΦB has reverse signs. Here, Lenz’s law formula is shown below:

Lenz’s Law Formula **Emf = -N (ΔΦ/ Δt)**

Where:

‘Emf’ = Induced voltage or electromotive force.

‘N’ = The number of loops.

‘Δϕ’ = Change within magnetic flux.

‘Δt’ = Change within time.

#### Lenz’s Law & Conservation of Energy

The induced current direction through Lenz’s law must generate a magnetic field to obey the energy conservation that restricts the magnetic field that produced it. This law is an outcome of the energy conservation law.

Once the magnetic field formed through the current induced will be in a similar direction like the field generated it, after that these magnetic fields would merge to make a bigger magnetic field.

This magnetic field will induce one more current in the conductor to twice the induced current’s magnitude. Thus, we can conclude that if Lenz’s law did not state that the induced current should form a magnetic field to restrict the created field, then we would finish up with a nonstop positive feedback loop for breaking the protection of energy.

This law generally obeys Newton’s 3rd law of motion, which states that for each action there is always an equivalent and reverse reaction. If the induced current forms a magnetic field that is equivalent and reverse to the magnetic field’s direction that makes it, then only it resists the magnetic field change within the region.

### Experiment

This **Lenz’s law experiment** is mainly for discovering the induced electromotive force direction & current we look for Lenz’s law. For this law, the following three experiments were proved through his theory.

#### 1st Experiment

In this experiment, Emil Lenz said that when the current flows within the coil of the circuit then generate magnetic field lines. When the current supply within the coil increases, the magnetic flux will be increased. So, the induced current flow direction will restrict once the magnetic flux enhances.

#### 2nd Experiment

In this 2nd experiment, Lenz declared that once the current-carrying coil is wounded over an iron rod using his left end which acts like an N-pole & is turned toward the ‘S’ coil, then an induced current will be generated.

#### 3rd Experiment

In this 3rd experiment, Lenz stated that once the coil is dragged in the direction of the magnetic flux, then the coil which is associated through it decreases. So, based on Lenz’s law, the coil’s motion is restricted once the induced current is provided within a similar direction.

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

### Lenz’s Law Problems and Solutions

1). A circular shape wire coil including 350 turns & a 7.5 cm radius is located horizontally over a table. A consistent magnetic field positioning openly up is gradually switched on, so the magnetic field strength can be expressed like a time function as B(t) = 0.02(T /s2) ×t2. So, what is the complete EMF within the coil like a function of time, and in which way does the current supply?

**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 T x t**

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

**= -25 t V/s**

In clockwise direction it supplies.

2). If the flow of current within a wire is from B to A direction then find out the induced current direction within the metallic loop wire kept aside as shown in the following figure.

Based on Lenz’s law, the induced current direction will restrict the cause of its production. Thus, the current flow within a loop will induce to support the flow of current within the wire which means in a similar direction. As a result, the current direction within the loop will be in a clockwise direction.

3). In a circular loop, resistance ‘R’ and area ‘A’ turns through an angular velocity ‘ω’ on an axis throughout its diameter is shown below. The loop’s plane is primarily perpendicular to a stable magnetic field ‘B’. Please find the induced current within the circle loop.

The direct magnetic flux throughout the loop is

**ΦB = BA cos θ**

**Here, θ = ωt, thus, ΦB = BA cos ωt**

According to Faraday’s law,

**ϵ = −dΦB/dt = – ϵ = −d/dt [BA cosωt]**

**or**

**ϵ = [BAω sinωt]**

The current induced can be expressed as

**I = E/R = (BAω/R) sinωt**

Here, both the current & the induced emf change sinusoidally. So, the emf amplitude is ‘BAω’ & the current is BAω/R.

### Advantages

The **significance of Lenz’s law** includes the following.

- Lenz’s law tells us two main things regarding how the magnetic field changing will interact with a conductor loop.
- This law depends on energy conservation but not on the momentum conservation
- This law is available to rule how magnetic fields are generated through conductors carrying AC or DC.
- This law states an induced current’s direction to the rate of change within the inducing magnetic field.
- In electromagnetism, this law is a very significant concept

#### Limitations of Lenz’s Law

The **limitations of Lenz’s Law** include the following.

Once a magnet is moved in the direction of the coil, then the exterior magnet field will induce a current within the coil to make its inside magnet field through a similar magnitude however with the reverse direction, hence opposing the change.

Once the magnet moves through the coil or other face of the coil, then the flow of current will change the direction & the inside magnetic field will be enhanced within a similar direction due to the external magnetic field, so again opposing the change.

### Where is Lenz’s law used/Applications?

The applications of Lenz’s law include the following.

- This law is very helpful in understanding the stored magnetic energy concept within an inductor
- Whenever an emf source is connected across an inductor, then-current starts flowing through it, and back emf will restrict the increasing flow of current throughout the inductor. To create the current flow, the exterior emf source has to do some work to conquer this opposition. So this work can be done through the stored emf within the inductor & it can be improved once the external source of emf is detached from the circuit.
- Lenz’s law specifies that the induced emf & the change within flux have reverse signs which give a physical understanding of the alternative of a sign within Faraday’s law of electromagnetic induction.
- This law applies to electric generators. Once the flow of current is induced within a generator, the then induced current direction will oppose & makes the generator rotate. Thus, the generator needs more mechanical energy to provide back emf while using an electric motor.
- It is used in induction cooktops & electromagnetic braking.
- It is used in AC generators & electric generators
- Used in metal detectors
- Eddy current dynamometers
- Used in braking systems of train
- Microphones
- Card Readers

**1). How Lenz Law is a Consequence of Conservation of Energy?**

Lenz’s law mainly depends on the concept of energy conservation. We know that in Lenz law the current induced is frequently tends to restrict the source which generates it. Thus, to do work against opposing forces we need to put some additional effort. So this additional work is direct to periodic change within magnetic flux so a huge current will be induced. Therefore, the additional effort is simply changed into electrical energy which is conservation of energy law.

**2). What is Lenz law Igcse?**

The Igcse board stands for “International General Certificate of Education” and this law from this board states that the current which is induced is always supplied in such a way that to oppose the motion or charge generating it.

**3). What happens if Lenz law is reversed?**

If Lenz’s law is simply reversed then the induced current generates flux in a similar direction like the original change. So this high change within the flux can generate an even larger current, followed through a still bigger change within flux. The flow of current will continue to rise indefinitely for generating power even after the creative stimulus is finished.

**4). What is the prime importance of Lenz’s law?**

This law is mainly used for determining the induced current’s direction

**5). What does the negative sign indicate in Lenz’s law?**

In Lenz’s law, the negative sign mainly specifies that the emf induced within the coil is in the reverse direction of the magnetic flux. Here this flux is connected through the coil.

Thus, this is all about an overview of Lenz’s Law discovered by Friedrich Emil Lenz. This law mainly depends on the conservation of energy principle & also Newton’s third law. So, it is the most suitable technique to conclude the induced current direction. He also discovered that the magnetic field’s strength is proportional to the power of the magnetic induction. Here is a question for you, what is Faraday’s Law of electromagnetic induction?