Faraday’s law of induction states that a changing magnetic flux through a circuit induces an electromotive force (emf) in the circuit. It is one of the fundamental laws of electromagnetism and explains how changing magnetic fields produce electric effects.
In its common circuit form, Faraday’s law relates the induced emf to the rate of change of magnetic flux:
ε = −dΦB/dt
For a coil of N identical turns:
ε = −N dΦB/dt
Here, ε is the induced emf, ΦB is magnetic flux, and t is time. The negative sign expresses Lenz’s law: the induced emf has a direction such that any resulting current opposes the change in magnetic flux that produced it.
Faraday’s law is the physical principle behind electric generators, transformers, induction cooktops, wireless charging, electromagnetic pickups, and many other technologies. Its local field form is the Maxwell-Faraday equation, one of Maxwell’s equations.
Key Takeaways: Faraday’s Law of Induction
- Faraday’s law of induction states that changing magnetic flux induces an electromotive force (emf).
- The basic equation is ε = −dΦB/dt, or ε = −N dΦB/dt for a coil of N turns.
- Magnetic flux changes when the magnetic field strength, loop area, or orientation of the loop changes.
- The negative sign comes from Lenz’s law and gives the direction of the induced emf.
- A changing magnetic field can induce emf even when the conductor does not move.
- A conductor moving through a magnetic field can also develop a motional emf.
- Faraday’s flux rule is particularly useful for analyzing circuits, while the Maxwell-Faraday equation describes electromagnetic induction locally in terms of electric and magnetic fields.
- Faraday’s law is fundamental to generators, transformers, inductors, induction heating, wireless charging, and many sensing technologies.
- Electromagnetic induction is also central to electromagnetic waves because changing electric and magnetic fields are coupled through Maxwell’s equations.
Why Faraday’s Law Is Important
Faraday’s law is important because it establishes one of the fundamental connections between electricity and magnetism: a changing magnetic environment can produce an electric effect.
Before the discovery of electromagnetic induction, electric currents were known to create magnetic fields. Faraday demonstrated the complementary phenomenon that changing magnetic conditions could generate electrical effects.
This discovery made large-scale electrical power generation possible. In an electric generator, mechanical energy changes the magnetic flux through conducting coils, inducing an emf. Nearly all conventional electrical generating systems ultimately depend on this principle, whether their mechanical energy comes from steam turbines, flowing water, wind turbines, or other sources.
Faraday’s law also explains transformer operation. Transformers use changing magnetic flux to transfer electrical energy between circuits and change voltage and current levels. This ability is fundamental to electrical power transmission and distribution.
More fundamentally, Faraday’s law became one of Maxwell’s equations and helped establish the modern electromagnetic field theory that describes electricity, magnetism, light, and other electromagnetic radiation.
History of Faraday’s Law
The discovery of electromagnetic induction grew out of experiments showing a relationship between electricity and magnetism.
Ørsted and Ampère
In 1820, Danish physicist Hans Christian Ørsted discovered that an electric current deflects a compass needle, demonstrating that electric currents produce magnetic effects.
Soon afterward, André-Marie Ampère investigated the forces between electric currents and developed important mathematical descriptions of electromagnetism.
These discoveries raised an obvious question: if electricity produces magnetism, could magnetism produce electricity?
Faraday’s Experiments
British scientist Michael Faraday answered this question experimentally in 1831.
In one famous experiment, Faraday wound two coils of wire around an iron ring. One coil was connected to a battery and the other to a galvanometer. Faraday found that connecting or disconnecting the battery produced a brief current in the second coil.
A steady current in the first coil did not continuously produce current in the second. Instead, induction occurred when the magnetic conditions were changing.
Faraday also discovered that moving a magnet into or out of a coil induced a current. Reversing the direction of motion reversed the current.
These experiments established the essential principle of electromagnetic induction.
Faraday’s Disk
Faraday also constructed an early electromagnetic generator known as the Faraday disk. A conducting disk rotated in a magnetic field, producing an emf between its center and rim.
The experiment demonstrated that mechanical motion in a magnetic field could generate electrical energy.
Lenz’s Law
In 1834, physicist Heinrich Lenz formulated the rule now called Lenz’s law. It determines the direction of induced current:
An induced current flows in the direction that opposes the change in magnetic flux that caused it.
This principle accounts for the negative sign in the mathematical form of Faraday’s law.
Maxwell’s Contribution
During the 1860s, James Clerk Maxwell incorporated Faraday’s experimental discoveries into his mathematical theory of electromagnetism.
The resulting Maxwell-Faraday equation expresses electromagnetic induction as a relationship between changing magnetic fields and circulating electric fields.
Maxwell’s equations ultimately predicted electromagnetic waves and demonstrated that light itself is an electromagnetic phenomenon.
What Is Faraday’s Law of Induction?
Faraday’s law of induction describes the relationship between changing magnetic flux and induced electromotive force.
In simple terms:
The faster magnetic flux through a circuit changes, the greater the induced emf.
The magnetic field itself does not necessarily have to be changing. What matters in the circuit form of the law is whether the magnetic flux through the circuit changes.
For example, induction occurs when:
- A magnet moves toward or away from a conducting loop.
- A conducting loop moves through a nonuniform magnetic field.
- A loop rotates in a magnetic field.
- The magnetic field strength through a stationary loop changes.
- The area enclosed by a circuit changes.
- The angle between a loop and the magnetic field changes.
This distinction is important. A strong but constant magnetic field through a stationary loop produces no induced emf if the magnetic flux remains constant.
Magnetic Flux
Understanding Faraday’s law requires understanding magnetic flux.
Magnetic flux measures the amount of magnetic field passing through a surface. It is defined as:
ΦB = ∫ B · dA
where:
- ΦB = magnetic flux
- B = magnetic field
- dA = infinitesimal area vector
For a uniform magnetic field passing through a flat surface:
ΦB = BA cos θ
where:
- B = magnetic field strength
- A = area of the surface
- θ = angle between the magnetic field and the surface’s normal vector
The SI unit of magnetic flux is the weber (Wb):
1 Wb = 1 T·m²
where T is the tesla.
A Common Angle Mistake
The angle θ is measured between the magnetic field and a line perpendicular to the surface, not between the magnetic field and the surface itself.
Therefore:
- Field perpendicular to the loop: θ = 0°, so ΦB = BA.
- Field parallel to the plane of the loop: θ = 90°, so ΦB = 0.
This convention is a frequent source of errors in introductory physics problems.
Formula for Faraday’s Law
For a single conducting loop:
ε = −dΦB/dt
For a coil containing N turns, where each turn experiences the same flux:
ε = −N dΦB/dt
where:
- ε = induced emf, in volts (V)
- N = number of turns
- ΦB = magnetic flux through one turn, in webers (Wb)
- t = time, in seconds (s)
For a finite time interval, the average induced emf is:
εavg = −N ΔΦB/Δt
The magnitude is:
|εavg| = N |ΔΦB|/Δt
Because:
1 V = 1 Wb/s
a rapidly changing magnetic flux produces a larger induced voltage than the same flux change occurring slowly.
What Does the Negative Sign Mean?
The negative sign in Faraday’s law represents Lenz’s law.
Suppose magnetic flux pointing into a loop is increasing. The induced current produces its own magnetic field that acts against this increase.
Similarly, if the original magnetic flux is decreasing, the induced current produces a field that tends to maintain it.
The induced effect therefore opposes the change in flux, rather than necessarily opposing the original magnetic field itself.
This distinction is important.
Lenz’s law is also a consequence of conservation of energy. If induced currents reinforced the changes that produced them, a system could potentially amplify its own motion and electrical output without an external energy source.
Instead, mechanical work is required to overcome the electromagnetic forces associated with induction. A generator converts this supplied mechanical energy into electrical energy.
Right-Hand Rules and Faraday’s Law
Right-hand rules help determine the directions of magnetic fields, induced currents, and magnetic forces in electromagnetic induction problems.
For a conducting loop, first use Lenz’s law to determine the direction of the magnetic field produced by the induced current. Then use the right-hand grip rule: curl the fingers of the right hand in the direction of conventional current around the loop, and the thumb points in the direction of the magnetic field through the loop.
For motional emf, the magnetic force on a positive charge is:
F = q(v × B)
Use the right-hand rule for the cross product v × B to determine the force on positive charges. The force on negative charges is in the opposite direction.
A useful problem-solving sequence is:
- Determine whether the magnetic flux is increasing or decreasing.
- Use Lenz’s law to find the direction of the induced magnetic field.
- Use the right-hand grip rule to find the direction of conventional current.
- For a moving conductor, use the v × B right-hand rule to determine charge separation or magnetic force.
What About the Left-Hand Rule?
Some textbooks use Fleming’s right-hand rule for generators and Fleming’s left-hand rule for motors. In Fleming’s right-hand generator rule, the thumb represents motion, the first finger represents the magnetic field, and the second finger represents induced conventional current.
Fleming’s left-hand rule applies primarily to the motor effect, where a current-carrying conductor experiences a force in a magnetic field. It is therefore less directly relevant to Faraday’s law of induction.
These rules are convenient mnemonics rather than additional physical laws. The more general relationships are Faraday’s law, Lenz’s law, and the Lorentz force law.
Faraday’s Law and Lenz’s Law
The terms Faraday’s law, Faraday-Lenz law, and Faraday’s flux rule are closely related.
Faraday’s law determines the magnitude of the induced emf from the rate of change of magnetic flux.
Lenz’s law specifies the direction of the induced emf or current.
Combining them gives:
ε = −dΦB/dt
The minus sign incorporates Lenz’s law into Faraday’s mathematical relationship.
Faraday’s Law vs the Maxwell-Faraday Equation
While Faraday’s flux rule and the Maxwell-Faraday equation are closely related, they should not always be treated as identical statements.
Faraday’s Flux Rule
For a circuit:
ε = −dΦB/dt
This relates the emf around a circuit to the changing magnetic flux through it.
For a stationary closed path, emf may be expressed as:
∮ E · dl = −d/dt ∫ B · dA
Maxwell-Faraday Equation
The differential form is:
∇ × E = −∂B/∂t
where:
- E = electric field
- B = magnetic field
- ∇ × E = curl of the electric field
This equation says that a magnetic field changing with time produces a circulating, non-conservative electric field.
The integral form for a fixed contour is:
∮ E · dl = −d/dt ∫ B · dA
Stokes’ theorem connects this integral equation to the differential Maxwell-Faraday equation.
Why the Distinction Matters
For a stationary circuit, the connection between changing magnetic flux and the Maxwell-Faraday equation is straightforward.
For a moving conductor, however, the emf can also involve the magnetic Lorentz force acting on charges:
F = q(E + v × B)
A conductor moving through a static magnetic field may experience a motional emf even though ∂B/∂t = 0.
So, the Maxwell-Faraday equation specifically describes how a time-varying magnetic field creates a circulating electric field, while the more general circuit treatment of electromagnetic induction may include both electric-field and motional contributions.
Two Main Ways to Produce Induced EMF
Introductory treatments often divide electromagnetic induction into transformer emf and motional emf.
Transformer EMF
Transformer emf occurs when a conductor remains stationary while the magnetic field through the circuit changes with time.
A changing magnetic field produces a circulating electric field according to:
∇ × E = −∂B/∂t
This electric field exerts forces on charges in the conductor.
A transformer is the classic example. Alternating current in a primary coil creates changing magnetic flux through a secondary coil, inducing an emf in the secondary.
Motional EMF
Motional emf occurs when a conductor moves through a magnetic field.
Charges moving with the conductor experience the magnetic Lorentz force:
F = q(v × B)
This force separates charges and can produce an emf.
For a straight conducting rod of length ℓ moving at speed v perpendicular to both its length and a uniform magnetic field:
ε = Bℓv
This equation applies to the standard geometry in which v, B, and the rod are mutually perpendicular.
Motional emf is fundamental to the operation of many electric generators.
A More General Expression for EMF
The distinction between transformer and motional emf becomes clearer using the Lorentz force.
For a moving circuit, the emf can be written as:
ε = ∮ (E + v × B) · dl
The E term accounts for electric forces, including electric fields produced by changing magnetic fields.
The v × B term accounts for magnetic forces on charges moving with the conductor.
Under appropriate conditions, this generalized expression leads to the familiar flux rule:
ε = −dΦB/dt
This formulation helps explain why induction can occur through several physically different mechanisms even when the same flux-rule equation successfully describes the circuit.
Worked Example 1: Changing Magnetic Field
A circular coil contains 200 turns and has an area of 0.010 m². A uniform magnetic field perpendicular to the coil decreases from 0.80 T to 0.20 T in 0.050 s. Find the magnitude of the average induced emf.
For a perpendicular field:
ΦB = BA
The change in flux through one turn is:
ΔΦB = AΔB
ΔΦB = (0.010 m²)(0.20 T − 0.80 T)
ΔΦB = −0.0060 Wb
Using Faraday’s law:
|εavg| = N |ΔΦB|/Δt
|εavg| = (200)(0.0060 Wb)/(0.050 s)
|εavg| = 24 V
Answer: 24 V
The magnetic flux is decreasing. Lenz’s law determines the direction of the induced current: its magnetic field acts to oppose that decrease.
Worked Example 2: Motional EMF
A conducting rod 0.50 m long moves at 8.0 m/s perpendicular to a uniform 0.30 T magnetic field. The rod, its velocity, and the field are mutually perpendicular. What emf develops across the rod?
Use:
ε = Bℓv
Substitute the values:
ε = (0.30 T)(0.50 m)(8.0 m/s)
ε = 1.2 V
Answer: 1.2 V
The polarity of the rod can be determined using the direction of v × B for positive charges.
Worked Example 3: Rotating Coil
A 100-turn coil with an area of 0.020 m² rotates in a uniform magnetic field of 0.50 T with angular speed ω.
The magnetic flux through one turn varies as:
ΦB = BA cos(ωt)
Faraday’s law gives:
ε = −N dΦB/dt
Differentiating:
ε = NBAω sin(ωt)
Therefore, the maximum emf is:
εmax = NBAω
This result explains the basic operation of an alternating-current generator. Rotating a coil in a magnetic field produces a sinusoidally varying emf.
Faraday’s Law and Electric Generators
One of the most important applications of Faraday’s law is the electric generator.
A generator changes magnetic flux through conducting coils, often by rotating a coil relative to a magnetic field or rotating a magnetic field relative to stationary windings.
For an ideal rotating coil:
ε = NBAω sin(ωt)
The resulting emf alternates direction periodically, producing alternating voltage.
The generator does not create energy. Mechanical work supplied by a turbine, engine, or other source is converted into electrical energy.
Lenz’s law explains why generating electricity creates an opposing torque. Increasing the electrical load on a generator generally requires greater mechanical input.
Faraday’s Law and Transformers
A transformer uses electromagnetic induction to transfer electrical energy between circuits.
An alternating current in the primary winding produces changing magnetic flux in a magnetic core. This changing flux passes through the secondary winding and induces an emf.
For an ideal transformer:
Vs/Vp = Ns/Np
where:
- Vs = secondary voltage
- Vp = primary voltage
- Ns = number of secondary turns
- Np = number of primary turns
A transformer can therefore step voltage up or down by changing the ratio of turns.
Transformers require changing magnetic flux, which is why conventional transformers operate with alternating or otherwise time-varying currents rather than steady direct current.
Self-Induction and Mutual Induction
Faraday’s law also explains self-induction and mutual induction.
Self-Induction
When current through a circuit changes, its own magnetic field changes. This changing field alters the magnetic flux through the circuit itself and produces an emf.
For an ideal inductor:
εL = −L di/dt
where L is the inductance.
The induced emf opposes the change in current.
Mutual Induction
When changing current in one circuit changes the magnetic flux through another circuit, it produces an emf in the second circuit.
For two coupled circuits:
ε₂ = −M di₁/dt
where M is the mutual inductance.
Transformer operation is based on mutual induction.
Eddy Currents
Faraday’s law also predicts eddy currents, which are circulating currents induced within bulk conductors exposed to changing magnetic flux.
According to Lenz’s law, their magnetic effects oppose the change that creates them.
Eddy currents have both useful and undesirable effects.
Useful applications include:
- Electromagnetic braking
- Induction heating
- Metal detectors
- Magnetic damping
- Some speedometers and measuring instruments
In transformers, motors, and generators, unwanted eddy currents waste energy as heat. Laminated or otherwise specially constructed magnetic cores help reduce these losses.
Applications of Faraday’s Law
Faraday’s law has an enormous range of practical applications.
Electric Generators
Generators convert mechanical energy into electrical energy by changing magnetic flux through conductors.
Transformers
Transformers use changing magnetic flux to transfer energy between circuits and step voltage up or down.
Induction Motors
Changing magnetic fields induce currents in conducting rotor components, producing electromagnetic forces and torque.
Induction Cooktops
Alternating magnetic fields induce eddy currents in suitable cookware. Electrical resistance converts the energy of these currents into heat.
Wireless Charging
Charging pads produce alternating magnetic fields that induce voltage in receiver coils within compatible devices.
Dynamic Microphones
Motion of a coil relative to a magnet induces a voltage corresponding to sound vibrations.
Electric Guitar Pickups
Vibrating ferromagnetic strings change magnetic flux through pickup coils, producing an electrical signal.
Magnetic Sensors
Induction coils detect changing magnetic fields and are used in scientific instruments, industrial equipment, and geophysical measurements.
Metal Detectors
Alternating magnetic fields induce currents in conducting objects. The fields generated by those currents alter the detector’s electromagnetic response.
Electromagnetic Brakes
Motion through magnetic fields induces eddy currents whose magnetic effects oppose the motion, producing non-contact braking.
Inductive Sensors
Industrial proximity and position sensors use electromagnetic induction to detect conductive objects without physical contact.
Faraday’s Law and Energy Conservation
Lenz’s law provides an important connection between electromagnetic induction and conservation of energy.
Consider pushing a magnet toward a conducting loop. The increasing magnetic flux induces a current whose magnetic field opposes the magnet’s approach.
The person pushing the magnet therefore has to perform work.
That mechanical energy becomes electrical energy in the circuit and may eventually become thermal energy through resistance.
If the induced current instead assisted the magnet’s motion, the magnet would accelerate while simultaneously producing electrical energy. This would violate conservation of energy.
Thus, the minus sign in Faraday’s law has profound physical meaning.
Faraday’s Law and Electromagnetic Waves
Faraday’s law is also essential to understanding electromagnetic radiation.
The Maxwell-Faraday equation states:
∇ × E = −∂B/∂t
So, a changing magnetic field is associated with a circulating electric field.
The Ampère-Maxwell law provides the complementary relationship in which changing electric fields contribute to magnetic fields.
Together with the other Maxwell equations, these relationships allow electric and magnetic disturbances to propagate through space as electromagnetic waves.
Light, radio waves, microwaves, infrared radiation, ultraviolet radiation, X-rays, and gamma rays are all electromagnetic waves.
Limitations and Conditions of Faraday’s Law
Faraday’s law is a fundamental law of classical electromagnetism rather than an approximate empirical rule with a simple breakdown point. However, the familiar equation:
ε = −N dΦB/dt
has assumptions and interpretive limitations that matter in practical applications.
The Simple Flux Formula Requires Care for Moving Circuits
For stationary circuits, changing magnetic fields produce electric fields described directly by the Maxwell-Faraday equation.
For moving circuits, magnetic Lorentz forces can also contribute to emf. A full treatment may require:
ε = ∮ (E + v × B) · dl
rather than attributing all induction to an electric field produced by ∂B/∂t.
Φ = BA cos θ Is Not Always Valid
The simple formula:
ΦB = BA cos θ
assumes a uniform magnetic field over a flat surface.
For nonuniform fields or curved surfaces, use:
ΦB = ∫ B · dA
NΦ Assumes Appropriate Flux Linkage
The expression:
ε = −N dΦB/dt
assumes that the turns are linked by the relevant magnetic flux in the manner represented by ΦB. Real coils can have leakage flux and nonuniform coupling.
Real Devices Are Not Ideal
Real generators, transformers, motors, and inductors have effects not captured by the simplest equations, including:
- Electrical resistance
- Eddy-current losses
- Magnetic hysteresis
- Leakage flux
- Parasitic capacitance
- Core saturation
- Skin and proximity effects
- Mechanical losses
Classical Electromagnetism Has a Domain of Applicability
Maxwell’s equations provide an extraordinarily accurate classical description of electromagnetic fields. At atomic and subatomic scales, electromagnetic interactions ultimately require quantum electrodynamics for a complete description.
This does not make Faraday’s law “wrong” at small scales. Rather, classical electromagnetic fields are an effective macroscopic description of a deeper quantum theory.
Faraday’s Law vs Related Laws
| Law | Main Idea |
|---|---|
| Faraday’s law | Changing magnetic flux induces emf |
| Lenz’s law | Induced effects oppose the change in magnetic flux |
| Maxwell-Faraday equation | Time-varying magnetic fields are associated with circulating electric fields |
| Lorentz force law | Electric and magnetic fields exert forces on charged particles |
| Ampère-Maxwell law | Currents and changing electric fields are associated with magnetic fields |
| Gauss’s law for electricity | Electric flux is related to enclosed electric charge |
| Gauss’s law for magnetism | Net magnetic flux through any closed surface is zero |
Together, these relationships form much of the foundation of classical electromagnetism.
Common Misconceptions About Faraday’s Law
A Magnetic Field Always Induces Current
False. A constant magnetic field through a stationary circuit does not induce an emf simply because the field exists.
The magnetic flux must change, or motion of the conductor must produce an equivalent motional effect.
The Magnetic Field Must Change Strength
Not necessarily.
Magnetic flux is:
ΦB = BA cos θ
So, flux changes if B, A, or θ changes.
A loop rotating in a constant magnetic field therefore experiences changing magnetic flux.
Induced EMF Always Means There Is a Current
No. An emf can exist even in an open circuit.
Current flows only when there is a closed conducting path, and its magnitude depends on the circuit’s impedance.
Lenz’s Law Says the Induced Field Opposes the Original Field
Not quite.
The induced effect opposes the change in magnetic flux, not necessarily the original magnetic field.
If the original flux is decreasing, for example, the induced field tends to reinforce the original field direction in order to oppose the decrease.
The Maxwell-Faraday Equation and Flux Rule Are Always Identical Statements
They are closely connected, but the distinction becomes important for moving circuits.
The Maxwell-Faraday equation describes the relationship between a time-varying magnetic field and the curl of the electric field. Motional emf can occur even in a static magnetic field through the magnetic part of the Lorentz force.
A Generator Creates Electrical Energy From a Magnetic Field
A generator converts mechanical energy into electrical energy.
The magnetic field enables electromagnetic energy conversion but is not an unlimited source of energy.
Faraday’s Law Violates Conservation of Energy
It does the opposite. Lenz’s law ensures that induced electromagnetic effects oppose the changes that produce them, consistent with conservation of energy.
Frequently Asked Questions
What is Faraday’s law in simple terms?
Faraday’s law says that changing magnetic flux through a circuit produces an electromotive force, or voltage.
What is the formula for Faraday’s law?
For one loop:
ε = −dΦB/dt
For N turns:
ε = −N dΦB/dt
What is magnetic flux?
Magnetic flux measures the magnetic field passing through a surface:
ΦB = ∫ B · dA
For a uniform field and flat surface:
ΦB = BA cos θ
What is the unit of magnetic flux?
The SI unit is the weber (Wb).
One weber equals one tesla-square meter:
1 Wb = 1 T·m²
What is the SI unit of induced emf?
The SI unit of emf is the volt (V).
Why is there a negative sign in Faraday’s law?
The negative sign represents Lenz’s law. It indicates that the induced emf acts in a direction that opposes the change in magnetic flux that produces it.
What causes electromagnetic induction?
Electromagnetic induction occurs when magnetic flux linked with a circuit changes or when motion through a magnetic field produces a motional emf.
Flux can change because of changes in magnetic field strength, circuit area, orientation, or relative motion.
Does a stationary magnet induce a current?
A stationary magnet and stationary loop generally do not produce a sustained induced emf because the magnetic flux is not changing.
Moving the magnet or loop relative to the other can change the flux and produce an emf.
Can a constant magnetic field induce an emf?
Yes, if a conductor moves through the field or if the circuit’s area or orientation changes so that magnetic flux changes.
A stationary circuit in a static magnetic field does not experience transformer emf.
What is motional emf?
Motional emf is an emf produced when a conductor moves through a magnetic field. In a common perpendicular geometry:
ε = Bℓv
What is transformer emf?
Transformer emf results from a time-varying magnetic field that produces a circulating electric field. This is the mechanism underlying transformer action.
Is Faraday’s law one of Maxwell’s equations?
The Maxwell-Faraday equation is one of Maxwell’s four equations. It expresses Faraday’s induction principle locally:
∇ × E = −∂B/∂t
The familiar circuit flux rule is closely related but requires care when the circuit itself moves.
What is the difference between Faraday’s law and Lenz’s law?
Faraday’s law relates induced emf to the rate of change of magnetic flux. Lenz’s law determines the direction of the induced effect. The negative sign in Faraday’s law incorporates Lenz’s law.
What is an everyday example of Faraday’s law?
Common examples include electrical generators, transformers, induction cooktops, wireless chargers, guitar pickups, dynamic microphones, and some electromagnetic braking systems.
Glossary
Electromagnetic Induction: Production of an emf as a result of changing magnetic flux or motion of a conductor through a magnetic field.
Electromotive Force (emf): Energy supplied or converted per unit charge around a circuit, measured in volts.
Magnetic Flux (ΦB): Measure of magnetic field passing through a surface.
Faraday’s Law: Relationship between induced emf and the rate of change of magnetic flux.
Faraday-Lenz Law: Faraday’s induction law written with the negative sign representing Lenz’s law.
Faraday’s Flux Rule: Circuit-level relationship between induced emf and changing magnetic flux.
Lenz’s Law: Rule stating that an induced effect acts in a direction that opposes the change in magnetic flux producing it.
Maxwell-Faraday Equation: Maxwell equation relating the curl of the electric field to the time rate of change of the magnetic field.
Motional EMF: EMF produced by the motion of a conductor through a magnetic field.
Transformer EMF: EMF associated with an electric field produced by a time-varying magnetic field.
Eddy Current: Circulating electric current induced within a bulk conductor by changing magnetic flux.
Inductance: Property describing the relationship between current and magnetic flux linkage in a circuit.
Self-Induction: Induction of an emf in a circuit caused by a change in its own current.
Mutual Induction: Induction of an emf in one circuit due to changing current in another circuit.
Weber (Wb): SI unit of magnetic flux.
References
- Faraday, Michael (1831). “Faraday’s notebooks: Electromagnetic Induction“. The Royal Institution of Great Britain.
- Lenz, Emil (1834). “Ueber die Bestimmung der Richtung der durch elektodynamische Vertheilung erregten galvanischen Ströme”. Annalen der Physik und Chemie. 107 (31): 483–494. doi:10.1002/andp.18341073103
- Sadiku, M. N. O. (2007). Elements of Electromagnetics (4th ed.). New York & Oxford: Oxford University Press. ISBN 978-0-19-530048-2.
- Tipler; Mosca (2004). Physics for Scientists and Engineers. Macmillan. ISBN 978-0-7167-0810-0.
- Zangwill, Andrew (2013). Modern Electrodynamics. Cambridge University Press. ISBN 978-0-521-89697-9.