Induced EMF and Current
3. Eddy Currents
Learning outcomes
- I can explain how eddy currents are produced.
- I can describe the effects of eddy currents in conductors.
- I can explain methods used to reduce unwanted eddy currents.
- I can identify useful applications of eddy currents.
- I can describe energy losses caused by eddy currents.
Eddy Currents
Eddy currents are circulating electric currents induced inside a solid conductor when the magnetic flux through the conductor changes.
Unlike current flowing through a wire in a circuit, eddy currents form closed loops within the conducting material itself. They are produced by electromagnetic induction and follow both Faraday's law and Lenz's law.
Eddy currents can be:
- useful, as in electromagnetic braking and induction heating
- unwanted, because they can waste energy as heat in transformers, motors, and generators
Understanding how eddy currents form allows engineers to either increase them when useful or reduce them when they cause energy losses.
How Eddy Currents Are Produced
Consider a solid metal plate moving through a magnetic field.
As different parts of the plate enter or leave the magnetic field, the magnetic flux through regions of the conductor changes.
According to Faraday's law:
changing magnetic flux → induced EMF
Because the metal is conducting, the induced EMF causes currents to circulate inside the metal.
These circulating currents are called:
eddy currents
The word eddy comes from the circular currents or whirlpools that can form in moving fluids.
Eddy Currents and Electromagnetic Induction
The same basic principle that induces current in a wire loop also produces eddy currents.
Faraday's law states:
ε = −ΔΦ/Δt
The negative sign represents Lenz's law.
In a wire loop, the conducting path is clearly defined by the wire.
In a solid sheet or block of metal, many possible conducting paths exist. The induced currents can therefore circulate through regions of the material itself.
Changing Magnetic Flux
Eddy currents can be produced whenever the magnetic flux through a conductor changes.
This can happen when:
- a conductor moves through a magnetic field
- a magnet moves relative to a conductor
- the magnetic field changes with time
- the conductor rotates in a magnetic field
- an alternating current creates a changing nearby magnetic field
The important condition is:
the magnetic flux must change
A stationary conductor in a constant magnetic field does not continuously produce eddy currents.
Lenz's Law and Eddy Currents
Eddy currents follow Lenz's law.
The magnetic field produced by the eddy currents acts to oppose the change in magnetic flux that created them.
Therefore:
change in magnetic flux → eddy current → opposing magnetic effect
This explains many of the unusual forces associated with eddy currents.
For example, a magnet moving over a conducting metal plate can experience a force opposing its motion.
Example: Magnet Approaching a Metal Plate
Suppose a magnet moves toward a conducting metal plate.
The magnetic flux through the plate increases.
Eddy currents form in the plate.
According to Lenz's law, these currents create their own magnetic field that opposes the increasing flux.
The resulting magnetic interaction tends to:
oppose the approaching magnet
The magnet therefore experiences a resistive force.
Magnet Moving Away
If the magnet moves away from the plate, the magnetic flux decreases.
The eddy currents reverse direction.
Their magnetic field now acts to oppose the decrease in flux.
The resulting force again tends to oppose the motion.
Therefore, whether the magnet approaches or moves away:
eddy-current forces resist the change producing them.
Magnetic Drag
The force caused by eddy currents is often called magnetic drag.
Unlike ordinary friction, magnetic drag does not necessarily require surfaces to touch.
A conductor can experience a braking force simply by moving through a magnetic field.
This allows braking systems to operate with:
- little physical contact
- reduced mechanical wear
- smooth braking forces
A Falling Magnet in a Metal Tube
A dramatic demonstration of eddy currents uses a strong magnet dropped through a conducting tube, such as a copper or aluminum tube.
The falling magnet produces changing magnetic flux in the tube.
Eddy currents form in the tube.
Their magnetic fields oppose the magnet's downward motion.
As a result, the magnet falls much more slowly than it would through a nonconducting tube.
Why the Magnet Does Not Simply Stop
The eddy currents oppose the magnet's motion, but they do not normally hold it permanently in place.
If the magnet stopped moving:
- the magnetic flux would stop changing
- the induced EMF would decrease
- the eddy currents would decrease
- the magnetic braking force would decrease
The magnet can therefore continue falling at a reduced speed.
This is another example of Lenz's law opposing a change, rather than simply opposing a magnetic field.
Factors Affecting Eddy Currents
The strength of eddy currents depends on several factors.
Important factors include:
- rate of change of magnetic flux
- magnetic field strength
- speed of relative motion
- electrical conductivity of the material
- thickness and shape of the conductor
- size of available current loops
A larger induced EMF and lower electrical resistance generally allow stronger eddy currents.
Effect of Magnetic Field Strength
A stronger magnetic field can produce a larger change in magnetic flux.
According to Faraday's law:
greater rate of flux change → greater induced EMF
This can produce stronger eddy currents.
Therefore, stronger magnetic fields generally produce stronger eddy-current effects when other conditions remain similar.
Effect of Speed
Suppose a conductor moves through a magnetic field.
Moving faster causes the magnetic flux to change more rapidly.
Therefore:
greater speed → greater rate of flux change → larger induced EMF
This generally produces stronger eddy currents and greater magnetic drag.
This is one reason eddy-current brakes can become particularly effective at higher speeds.
Effect of Electrical Conductivity
Materials with high electrical conductivity allow induced currents to flow more easily.
Metals such as:
- copper
- aluminum
can therefore support strong eddy currents.
Poor electrical conductors have greater resistance and generally produce weaker eddy currents.
Heating Caused by Eddy Currents
Real conductors have electrical resistance.
When eddy currents flow through a conductor, electrical energy is converted into thermal energy.
The heating effect can be described using:
P = I²R
where:
- P = thermal power
- I = current
- R = resistance
Therefore, eddy currents can cause a conductor to become warm or hot.
This heating can either be:
useful
or:
an unwanted energy loss
Energy Conservation
Eddy-current braking provides an important example of energy conservation.
Suppose a metal plate moves through a magnetic field.
The eddy currents produce magnetic forces opposing its motion.
The object loses kinetic energy.
That energy is mainly converted into:
thermal energy in the conductor
Therefore:
kinetic energy → electrical energy in eddy currents → thermal energy
The magnetic field does not destroy the energy.
It changes how the energy is transferred.
Unwanted Eddy Currents
Many electrical devices contain conducting metal parts exposed to changing magnetic fields.
Examples include:
- transformers
- motors
- generators
- electromagnets
Changing magnetic flux can produce unwanted eddy currents inside these components.
The resulting currents:
- heat the material
- waste energy
- reduce efficiency
- may damage equipment if excessive
Eddy Currents in Transformer Cores
A transformer contains coils carrying alternating current.
The alternating current creates a continuously changing magnetic field.
The transformer core is therefore exposed to changing magnetic flux.
If the core were one large solid piece of conducting metal, strong eddy currents could circulate through it.
These currents would produce unwanted heating.
Reducing Eddy Currents with Laminations
One of the most important methods of reducing unwanted eddy currents is lamination.
Instead of constructing a transformer core from one solid block, engineers build it from many thin sheets of magnetic material.
These sheets are called:
laminations
The layers are electrically insulated from one another.
How Laminations Work
A solid metal core provides large conducting paths through which eddy currents can circulate.
Laminating the core divides it into many thin sections.
This:
- breaks up large current loops
- reduces the area enclosed by each loop
- increases resistance to current flowing between layers
- greatly reduces eddy-current magnitude
As a result:
less electrical energy is converted into unwanted thermal energy
and the device becomes more efficient.
Solid Core vs Laminated Core
| Solid Core | Laminated Core |
|---|---|
| Large current loops possible | Current loops restricted |
| Stronger eddy currents | Weaker eddy currents |
| Greater heating | Less heating |
| Greater energy loss | Smaller energy loss |
| Lower efficiency | Higher efficiency |
Lamination does not completely eliminate eddy currents, but it can reduce them dramatically.
Why the Laminations Are Insulated
If the metal sheets were in good electrical contact with one another, currents could still flow from one layer to another and form larger loops.
A thin insulating coating between layers prevents this.
The magnetic field can still pass through the core, while electrical current is restricted.
This allows the core to maintain its magnetic function while reducing eddy-current losses.
Thin Laminations
Thinner laminations generally restrict eddy currents more effectively.
The current loops are forced into smaller paths.
However, practical engineering involves balancing:
- cost
- manufacturing difficulty
- mechanical strength
- magnetic performance
- required efficiency
The ideal thickness therefore depends on the application.
High-Resistivity Magnetic Materials
Another method of reducing eddy currents is to use materials with greater electrical resistance.
Greater resistance reduces the induced current.
Some electrical devices use specially designed magnetic materials that:
- respond strongly to magnetic fields
- have relatively high electrical resistivity
This reduces eddy-current heating.
Ferrite Cores
At high frequencies, many devices use ferrites.
Ferrites are magnetic ceramic materials with relatively high electrical resistance.
Because they conduct electricity poorly compared with ordinary metals, eddy currents are greatly reduced.
Ferrites are commonly used in applications such as:
- high-frequency transformers
- inductors
- electronic power supplies
- radio-frequency equipment
Slots and Segmentation
Eddy currents can also be reduced by physically interrupting possible current paths.
Engineers may use:
- slots
- thin sections
- segmented conductors
- insulated layers
These features prevent large circulating currents from developing.
The general principle is:
break up the current path → reduce eddy currents
Useful Eddy Currents
Eddy currents are not always undesirable.
Many technologies deliberately create strong eddy currents because their:
- magnetic forces
- heating effects
can be useful.
Major applications include:
- electromagnetic braking
- induction heating
- metal detection
- speed sensing
- damping instruments
- nondestructive testing
Eddy-Current Brakes
An eddy-current brake uses magnetic fields to slow a moving conductor.
For example, a metal disk may rotate through a magnetic field.
As the disk moves:
- magnetic flux through regions of the disk changes
- eddy currents form
- their magnetic fields oppose the motion
- the disk slows
No friction pad needs to press directly against the disk to create the braking force.
Advantages of Eddy-Current Braking
Eddy-current brakes can provide:
- smooth braking
- rapid response
- little mechanical wear
- reduced maintenance
- contactless operation
- reliable braking at high speeds
They are useful in systems where reducing mechanical wear is important.
Limitations of Eddy-Current Braking
Eddy-current braking also has limitations.
At very low speeds:
- magnetic flux changes more slowly
- induced EMF becomes smaller
- eddy currents become weaker
- braking force decreases
At zero relative motion, ordinary eddy-current braking cannot maintain a braking force because there is no changing flux.
Therefore, some systems still require mechanical brakes for stopping completely or holding a stationary object.
Transportation Applications
Eddy-current braking has been used or investigated in systems such as:
- trains
- roller coasters
- exercise equipment
- industrial machinery
- high-speed rotating equipment
The conductor and magnet do not need to rub against one another.
This reduces wear compared with purely friction-based braking.
Induction Heating
Eddy currents can deliberately be used to produce heat.
An alternating current in a coil produces a changing magnetic field.
If a conductor is placed in this field:
- changing flux induces eddy currents
- the currents flow through the resistance of the material
- electrical energy becomes thermal energy
This is called induction heating.
Induction Cooktops
An induction cooktop contains a coil beneath the cooking surface.
Alternating current flows through the coil.
This creates a rapidly changing magnetic field.
Suitable cookware placed above the coil experiences changing magnetic flux.
Currents are induced within the cookware.
The cookware's electrical resistance converts energy into heat.
Therefore, much of the heating occurs directly in the cookware rather than by first heating an exposed electrical element.
Industrial Induction Heating
Induction heating is also used in manufacturing.
Applications can include:
- heating metal before shaping
- heat treatment
- hardening metal surfaces
- melting metals
- brazing and joining
- manufacturing processes
The ability to heat conductive materials without direct contact can provide precise and rapid heating.
Metal Detectors
Changing magnetic fields can induce eddy currents in nearby metal objects.
The eddy currents create their own magnetic fields.
A metal detector can detect changes caused by these secondary magnetic fields.
This principle is used in:
- security screening
- locating buried objects
- industrial inspection
- sorting materials
Eddy-Current Testing
Eddy currents can also be used for nondestructive testing.
A changing magnetic field induces currents in a conductive material.
If the material contains:
- cracks
- corrosion
- defects
- changes in thickness
the paths of the eddy currents are disturbed.
Sensors can detect these changes.
This allows some materials to be inspected without cutting them apart or damaging them.
Damping in Measuring Instruments
Eddy currents can be used to stop unwanted oscillations.
Suppose a metal component swings through a magnetic field.
Its motion produces eddy currents.
The resulting magnetic force opposes the motion.
The oscillation therefore dies away more quickly.
This is called electromagnetic damping.
It can help measuring instruments settle rapidly to a stable reading.
Speed Sensors
Eddy-current effects can also be used to detect motion or rotational speed.
A moving conducting component interacts with a magnetic field.
Changes in the resulting electromagnetic behaviour can provide information about:
- speed
- position
- rotation
This allows contactless measurements in some machines.
Eddy Currents and Mechanical Energy
Consider a rotating metal disk passing through a magnetic field.
Without the magnetic field, the disk may rotate for a long time.
With the magnetic field present:
- changing flux induces eddy currents
- the eddy currents produce magnetic fields
- magnetic forces oppose rotation
- the disk loses kinetic energy
- the disk and nearby components become slightly warmer
Thus:
mechanical energy → thermal energy
Why Eddy Currents Cause Energy Losses
Suppose a transformer core develops eddy currents.
The transformer is intended to transfer electrical energy from one circuit to another.
Instead, some energy is converted into thermal energy inside the core.
Therefore:
useful electrical energy → unwanted thermal energy
This reduces efficiency.
If:
P_in = input power
and:
P_useful = useful output power
then:
efficiency = P_useful/P_in × 100%
Reducing eddy-current losses can increase efficiency.
Example: Transformer Efficiency
A transformer receives:
500 W
of input power.
Its useful output is:
460 W
Suppose the remaining energy is lost through heating and other effects.
Total power loss:
P_loss = 500 − 460
P_loss = 40 W
Efficiency:
efficiency = 460/500 × 100%
efficiency = 92%
Reducing eddy-current heating could help increase this efficiency.
Eddy Currents and Joule Heating
The heating caused by an electric current is often called Joule heating.
The power dissipated is:
P = I²R
This equation shows why strong eddy currents can produce significant heating.
However, simply increasing resistance does not automatically mean greater eddy-current heating because the resistance also affects how much induced current can flow.
In devices where eddy currents are unwanted, engineers design the material and geometry so that the currents themselves become much smaller.
Why Cutting the Conductor Reduces Eddy Currents
Imagine a broad metal sheet in which a large circular eddy current can form.
Now imagine cutting narrow slots into the sheet.
The current can no longer follow the same large circular path.
It must:
- follow smaller paths
- take more resistive routes
- or be prevented from circulating altogether
This reduces the eddy-current effect.
The same basic idea explains why laminations are effective.
Comparing Useful and Unwanted Eddy Currents
| Situation | Eddy Currents | Desired Effect |
|---|---|---|
| Transformer core | Unwanted | Minimize heating |
| Motor core | Usually unwanted | Improve efficiency |
| Generator core | Usually unwanted | Reduce energy loss |
| Electromagnetic brake | Useful | Produce braking force |
| Induction cooktop | Useful | Produce heat |
| Metal detector | Useful | Detect conductive objects |
| Eddy-current testing | Useful | Detect defects |
| Damping system | Useful | Reduce oscillations |
Whether eddy currents are considered useful or harmful depends on the purpose of the device.
Relationship to Motional EMF
Motional EMF occurs when a conductor moves through a magnetic field.
Eddy currents can arise from the same process.
For example, when a metal disk rotates through a magnetic field:
- different parts of the disk move through the field
- motional EMFs develop
- circulating currents form within the disk
These are eddy currents.
Therefore, eddy currents connect directly with the earlier idea of motional EMF.
Relationship to Induction in Loops
In a conducting loop, changing magnetic flux produces an induced current along a clearly defined path.
In a solid conductor, there may be many possible paths.
Changing magnetic flux can therefore create circulating currents throughout the material.
The underlying principle is the same:
changing magnetic flux → induced EMF → current
The main difference is the geometry of the conducting path.
A Complete Reasoning Example
A solid aluminum disk rotates between the poles of a strong magnet.
Explain what happens.
First, sections of the disk move through the magnetic field.
The magnetic flux through regions of the disk changes.
Faraday's law predicts induced EMFs.
Because aluminum conducts electricity, circulating eddy currents form.
According to Lenz's law, the magnetic fields produced by these currents oppose the change that created them.
The disk therefore experiences a force opposing its rotation.
Its kinetic energy decreases.
Some of that energy becomes thermal energy in the disk because the eddy currents flow through electrical resistance.
Therefore:
the disk slows and becomes warmer.
A Complete Transformer Example
Consider a transformer with a solid iron core.
The alternating current in the primary coil creates a changing magnetic field.
The changing field passes through the conducting iron core.
Changing magnetic flux induces eddy currents in the core.
The currents encounter electrical resistance and produce heating.
This wastes energy.
Replacing the solid core with electrically insulated laminations breaks up the large current paths.
The eddy currents become much smaller.
Therefore:
- heating decreases
- energy loss decreases
- transformer efficiency increases
Designing to Increase Eddy Currents
When eddy currents are useful, designers may try to increase them.
Possible approaches include:
- using a strong magnetic field
- increasing the rate of flux change
- increasing relative speed
- using a good electrical conductor
- providing suitable paths for circulating current
For example, an eddy-current brake may use a highly conductive metal disk and strong magnets.
Designing to Reduce Eddy Currents
When eddy currents are unwanted, designers can reduce them by:
- laminating magnetic cores
- electrically insulating the laminations
- using higher-resistivity magnetic materials
- using ferrites at high frequencies
- cutting slots into conducting components
- segmenting conducting structures
- reducing unnecessary conducting loop areas
The central design principle is:
make large circulating currents difficult to form.
A Reliable Strategy for Eddy-Current Questions
First identify what causes the changing magnetic flux.
Ask:
- Is a conductor moving?
- Is a magnet moving?
- Is the magnetic field changing?
- Is alternating current producing the field?
Then identify the induced current.
Remember:
changing flux → induced EMF → eddy currents
Next apply Lenz's law:
the induced magnetic effect opposes the change
Finally, identify the energy transfer.
If the eddy currents are unwanted:
electrical/mechanical energy → unwanted thermal energy
If they are useful, identify the intended effect, such as:
- braking
- heating
- sensing
- damping
Common Mistakes
Thinking eddy currents require a wire loop
They can circulate inside a solid conducting material.
Thinking a constant magnetic field automatically produces eddy currents
There must be changing magnetic flux or relative motion that changes the flux experienced by the conductor.
Thinking eddy currents always oppose the magnetic field
They oppose the change in magnetic flux, according to Lenz's law.
Assuming eddy currents are always harmful
They are deliberately used in braking, heating, sensing, and testing.
Assuming eddy currents are always useful
In transformers, motors, and generators they can cause unwanted heating and reduce efficiency.
Thinking laminations prevent magnetic fields from entering the core
The purpose is mainly to restrict electrical current paths while allowing the core to perform its magnetic role.
Forgetting the insulation between laminations
Electrical insulation prevents currents from easily crossing between layers.
Thinking energy disappears during magnetic braking
Mechanical energy is mainly converted into thermal energy.
Assuming an eddy-current brake can always hold an object stationary
Ordinary eddy-current braking weakens as relative speed approaches zero.
Key Terms
Eddy current — circulating electric current induced within a bulk conductor by changing magnetic flux.
Electromagnetic induction — production of an EMF due to changing magnetic flux.
Magnetic flux — measure of the magnetic field passing through a surface.
Induced EMF — potential difference produced by electromagnetic induction.
Faraday's law — relationship between induced EMF and the rate of change of magnetic flux.
Lenz's law — principle stating that induced magnetic effects oppose the change that produced them.
Magnetic drag — resistive force caused by electromagnetic effects such as eddy currents.
Joule heating — conversion of electrical energy into thermal energy when current flows through resistance.
Lamination — thin, electrically insulated layer used to restrict eddy-current paths.
Ferrite — magnetic ceramic material with high electrical resistance, useful for reducing eddy currents at high frequencies.
Electromagnetic braking — use of magnetic induction to create a force opposing motion.
Induction heating — heating a conductor using currents induced by changing magnetic fields.
Electromagnetic damping — reduction of unwanted motion or oscillation using induced currents and opposing magnetic forces.
Nondestructive testing — inspection of a material for defects without significantly damaging it.
Energy loss — transfer of energy away from the intended useful pathway, often into thermal energy.
Key Takeaways
- Eddy currents are circulating currents induced inside conducting materials.
- They are produced when magnetic flux through regions of a conductor changes.
- Eddy currents are an example of electromagnetic induction.
- Faraday's law explains how changing magnetic flux produces induced EMF.
- Lenz's law determines the opposing nature of the resulting magnetic effects.
- A moving conductor can develop eddy currents when it passes through a magnetic field.
- A changing magnetic field can produce eddy currents even if the conductor itself is stationary.
- Stronger and more rapidly changing magnetic fields can produce stronger eddy-current effects.
- Good electrical conductors can support large eddy currents.
- Eddy currents produce magnetic fields of their own.
- These magnetic fields can produce forces that oppose motion.
- Magnetic braking converts kinetic energy mainly into thermal energy.
- Eddy currents can cause unwanted heating in transformers, motors, and generators.
- These losses reduce the efficiency of electrical machines.
- Laminated cores reduce eddy currents by breaking large conducting paths into smaller ones.
- Electrical insulation between laminations prevents currents from easily crossing between layers.
- High-resistivity magnetic materials and ferrites can also reduce eddy-current losses.
- Eddy currents are useful in electromagnetic brakes.
- Eddy currents are deliberately produced in induction heating and induction cooking.
- Metal detectors and nondestructive testing systems can detect the magnetic effects of eddy currents.
- Eddy currents can provide contactless damping of moving systems.
- Whether eddy currents are useful or unwanted depends on how their forces and heating effects are used.
Check Your Understanding
- What is an eddy current, and how does it differ from current flowing through an ordinary wire circuit?
- Explain why changing magnetic flux is necessary for producing eddy currents.
- A strong magnet moves toward a conducting aluminum plate. Explain how eddy currents form and how they affect the magnet's motion.
- Why does a magnet fall slowly when dropped through a conducting copper tube?
- Explain why the eddy-current braking effect becomes weaker as the relative speed approaches zero.
- State three factors that can increase the strength of eddy-current effects.
- Explain how eddy currents cause thermal energy to be produced in a conductor.
- Why are eddy currents usually undesirable inside transformer cores?
- Explain how laminating a transformer core reduces eddy-current losses.
- Why are the individual laminations electrically insulated from one another?
- Explain why ferrites can be useful in high-frequency electrical equipment.
- Describe how an eddy-current brake slows a rotating metal disk and identify the main energy transfer involved.
- Explain how an induction cooktop uses eddy-current effects to heat cookware.
- Compare the role of eddy currents in a transformer core, an electromagnetic brake, and an induction cooktop. In each case, state whether the eddy currents are useful or unwanted.
- An engineer is designing a device containing a conducting metal component exposed to a rapidly changing magnetic field. Describe at least three design changes that could reduce unwanted eddy-current heating, and explain why each change would help.