# Faraday's Law of Induction and Lenz' Law

## Faraday’s law of induction states that the EMF induced by a change in magnetic flux is $EMF = -N\frac{\Delta \Phi}{\Delta t}$, when flux changes by ΔΦ in a time Δt.

#### Key Points

• The minus in the Faraday's law means that the EMF creates a current I and magnetic field B that oppose the change in flux ΔΦ—this is known as Lenz’ law.

• Faraday's law of induction is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators, and solenoids.

• Faraday’s law states that the EMF induced by a change in magnetic flux depends on  the change in flux ΔΦ, time Δt, and number of turns of coils.

#### Terms

• (EMF)—The voltage generated by a battery or by the magnetic force according to Faraday's Law. It is measured in units of volts, not newtons, and thus, is not actually a force.

• A coil of wire that acts as a magnet when an electric current flows through it.

• The rate of transfer of energy (or another physical quantity) through a given surface, specifically electric flux or magnetic flux.

#### Figures

1. ##### Lenz' Law

(a) When this bar magnet is thrust into the coil, the strength of the magnetic field increases in the coil. The current induced in the coil creates another field, in the opposite direction of the bar magnet’s to oppose the increase. This is one aspect of Lenz’s law—induction opposes any change in flux. (b) and (c) are two other situations. Verify for yourself that the direction of the induced Bcoil shown indeed opposes the change in flux and that the current direction shown is consistent with the right hand rule.

Faraday's law of induction is a basic law of electromagnetism that predicts how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF). It is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators, and solenoids.

Faraday’s experiments showed that the EMF induced by a change in magnetic flux depends on only a few factors. First, EMF is directly proportional to the change in flux ΔΦ. Second, EMF is greatest when the change in time Δt is smallest—that is, EMF is inversely proportional to Δt. Finally, if a coil has N turns, an EMF will be produced that is N times greater than for a single coil, so that EMF is directly proportional to N. The equation for the EMF induced by a change in magnetic flux is

$EMF = -N\frac{\Delta \Phi}{\Delta t}$.

This relationship is known as Faraday’s law of induction. The units for EMF are volts, as is usual.

## Lenz' Law

The minus sign in Faraday’s law of induction is very important. The minus means that the EMF creates a current I and magnetic field B that oppose the change in flux ΔΦ—this is known as Lenz’ law. The direction (given by the minus sign) of the EMF is so important that it is called Lenz’ law after the Russian Heinrich Lenz (1804–1865), who, like Faraday and Henry, independently investigated aspects of induction. Faraday was aware of the direction, but Lenz stated it, so he is credited for its discovery (Figure 1).

## Energy Conservation

Lenz’ law is a manifestation of the conservation of energy. The induced EMF produces a current that opposes the change in flux, because a change in flux means a change in energy. Energy can enter or leave, but not instantaneously. Lenz’ law is a consequence. As the change begins, the law says induction opposes and, thus, slows the change. In fact, if the induced EMF were in the same direction as the change in flux, there would be a positive feedback that would give us free energy from no apparent source—conservation of energy would be violated.

#### Key Term Glossary

circuit
A pathway of electric current composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. T
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conservation
A particular measurable property of an isolated physical system does not change as the system evolves.
##### Appears in these related concepts:
current
The time rate of flow of electric charge.
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electromotive force
(EMF)—The voltage generated by a battery or by the magnetic force according to Faraday's Law. It is measured in units of volts, not newtons, and thus, is not actually a force.
##### Appears in these related concepts:
energy
A quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent.
##### Appears in these related concepts:
equation
An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; from which one is to determine a particular quantity.
##### Appears in these related concepts:
flux
The rate of transfer of energy (or another physical quantity) through a given surface, specifically electric flux or magnetic flux.
##### Appears in these related concepts:
force
A physical quantity that denotes ability to push, pull, twist or accelerate a body which is measured in a unit dimensioned in mass × distance/time² (ML/T²): SI: newton (N); CGS: dyne (dyn)
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Force
A force is any influence that causes an object to undergo a certain change, either concerning its movement, direction or geometrical construction.
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induction
The generation of an electric current by a varying magnetic field.
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inductor
A passive device that introduces inductance into an electrical circuit.
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Inductor
A device or circuit component that exhibits significant self-inductance; a device which stores energy in a magnetic field.
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Law
A concise description, usually in the form of a mathematical equation, used to describe a pattern in nature
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magnetic field
A condition in the space around a magnet or electric current in which there is a detectable magnetic force, and where two magnetic poles are present.
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magnetic flux
A measure of the strength of a magnetic field in a given area.
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positive feedback
a feedback loop in which the output of a system is amplified with a net positive gain each cycle.
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solenoid
A coil of wire that acts as a magnet when an electric current flows through it.
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transformer
A static device that transfers electric energy from one circuit to another by magnetic coupling. Their main use is to transfer energy between different voltage levels, which allows choosing most appropriate voltage for power generation, transmission and distribution separately.