Eddy currents are circular electric currents
induced within conductors by a changing magnetic
field in the conductor, due to Faraday's law
of induction. Eddy currents flow in closed
loops within conductors, in planes perpendicular
to the magnetic field. They can be induced
within nearby stationary conductors by a time-varying
magnetic field created by an AC electromagnet
or transformer, for example, or by relative
motion between a magnet and a nearby conductor.
The magnitude of the current in a given loop
is proportional to the strength of the magnetic
field, the area of the loop, and the rate
of change of flux, and inversely proportional
to the resistivity of the material.
By Lenz's law, an eddy current creates a magnetic
field that opposes the magnetic field that
created it, and thus eddy currents react back
on the source of the magnetic field. For example,
a nearby conductive surface will exert a drag
force on a moving magnet that opposes its
motion, due to eddy currents induced in the
surface by the moving magnetic field. This
effect is employed in eddy current brakes
which are used to stop rotating power tools
quickly when they are turned off. The current
flowing through the resistance of the conductor
also dissipates energy as heat in the material.
Thus eddy currents are a source of energy
loss in alternating current inductors, transformers,
electric motors and generators, and other
AC machinery, requiring special construction
such as laminated magnetic cores to minimize
them. Eddy currents are also used to heat
objects in induction heating furnaces and
equipment, and to detect cracks and flaws
in metal parts using eddy-current testing
instruments.
Origin of term
The term eddy current comes from analogous
currents seen in water when dragging an oar
breadthwise: localised areas of turbulence
known as eddies give rise to persistent vortices.
Somewhat analogously, eddy currents can take
time to build up and can persist for very
short times in conductors due to their inductance.
History
The first person to observe current eddies
was François Arago, the 25th Prime Minister
of France, who was also a mathematician, physicist
and astronomer. In 1824 he observed what has
been called rotatory magnetism, and that most
conductive bodies could be magnetized; these
discoveries were completed and explained by
Michael Faraday.
In 1834, Heinrich Lenz stated Lenz's law,
which says that the direction of induced current
flow in an object will be such that its magnetic
field will oppose the magnetic field that
caused the current flow. Eddy currents produce
a secondary field that cancels a part of the
external field and causes some of the external
flux to avoid the conductor.
French physicist Léon Foucault is credited
with having discovered eddy currents. In September,
1855, he discovered that the force required
for the rotation of a copper disc becomes
greater when it is made to rotate with its
rim between the poles of a magnet, the disc
at the same time becoming heated by the eddy
current induced in the metal. The first use
of eddy current for non-destructive testing
occurred in 1879 when David E. Hughes used
the principles to conduct metallurgical sorting
tests.
Explanation
Eddy currents in conductors of non-zero resistivity
generate heat as well as electromagnetic forces.
The heat can be used for induction heating.
The electromagnetic forces can be used for
levitation, creating movement, or to give
a strong braking effect. Eddy currents can
also have undesirable effects, for instance
power loss in transformers. In this application,
they are minimized with thin plates, by lamination
of conductors or other details of conductor
shape.
Self-induced eddy currents are responsible
for the skin effect in conductors. The latter
can be used for non-destructive testing of
materials for geometry features, like micro-cracks.
A similar effect is the proximity effect,
which is caused by externally induced eddy
currents.
When a conductor moves through an inhomogeneous
field generated by a source, electromotive
forces can be generated around loops within
the conductor. These EMFs acting on the resistivity
of the material generate a current around
the loop, in accordance with Faraday's law
of induction. These currents dissipate energy,
and create a magnetic field that tends to
oppose changes in the current- they have inductance.
Eddy currents are created when a conductor
experiences changes in the magnetic field.
If either the conductor is moving through
a steady magnetic field, or the magnetic field
is changing around a stationary conductor,
eddy currents will occur in the conductor.
Both effects are present when a conductor
moves through a varying magnetic field, as
is the case at the top and bottom edges of
the magnetized region shown in the diagram.
Eddy currents will be generated wherever a
conducting object experiences a change in
the intensity or direction of the magnetic
field at any point within it, and not just
at the boundaries.
The swirling current set up in the conductor
is due to electrons experiencing a Lorentz
force that is perpendicular to their motion.
Hence, they veer to their right, or left,
depending on the direction of the applied
field and whether the strength of the field
is increasing or declining. The resistivity
of the conductor acts to damp the amplitude
of the eddy currents, as well as straighten
their paths. Lenz's law states that the current
swirls in such a way as to create an induced
magnetic field that opposes the phenomenon
that created it. In the case of a varying
applied field, the induced field will always
be in the opposite direction to that applied.
The same will be true when a varying external
field is increasing in strength. However,
when a varying field is falling in strength,
the induced field will be in the same direction
as that originally applied, in order to oppose
the decline.
An object or part of an object experiences
steady field intensity and direction where
there is still relative motion of the field
and the object, or unsteady fields where the
currents cannot circulate due to the geometry
of the conductor. In these situations charges
collect on or within the object and these
charges then produce static electric potentials
that oppose any further current. Currents
may be initially associated with the creation
of static potentials, but these may be transitory
and small.
Eddy currents generate resistive losses that
transform some forms of energy, such as kinetic
energy, into heat. This Joule heating reduces
efficiency of iron-core transformers and electric
motors and other devices that use changing
magnetic fields. Eddy currents are minimized
in these devices by selecting magnetic core
materials that have low electrical conductivity
or by using thin sheets of magnetic material,
known as laminations. Electrons cannot cross
the insulating gap between the laminations
and so are unable to circulate on wide arcs.
Charges gather at the lamination boundaries,
in a process analogous to the Hall effect,
producing electric fields that oppose any
further accumulation of charge and hence suppressing
the eddy currents. The shorter the distance
between adjacent laminations, the greater
the suppression of eddy currents.
The conversion of input energy to heat is
not always undesirable, however, as there
are some practical applications. One is in
the brakes of some trains known as eddy current
brakes. During braking, the metal wheels are
exposed to a magnetic field from an electromagnet,
generating eddy currents in the wheels. The
eddy currents meet resistance as charges flow
through the metal, thus dissipating energy
as heat, and this acts to slow the wheels
down. The faster the wheels are spinning,
the stronger the effect, meaning that as the
train slows the braking force is reduced,
producing a smooth stopping motion. Induction
heating makes use of eddy currents to provide
heating of metal objects.
Power dissipation of eddy currents
Under certain assumptions the power lost due
to eddy currents per unit mass for a thin
sheet or wire can be calculated from the following
equation:
where
P is the power lost per unit mass,
Bp is the peak magnetic field,
d is the thickness of the sheet or diameter
of the wire,
f is the frequency,
k is a constant equal to 1 for a thin sheet
and 2 for a thin wire,
ρ is the resistivity of the material, and
D is the density of the material.
This equation is valid only under the so-called
quasi-static conditions, where the frequency
of magnetisation does not result in the skin
effect; that is, the electromagnetic wave
fully penetrates the material.
Skin effect
In very fast-changing fields, the magnetic
field does not penetrate completely into the
interior of the material. This skin effect
renders the above equation invalid. However,
in any case increased frequency of the same
value of field will always increase eddy currents,
even with non-uniform field penetration.
The penetration depth for a good conductor
can be calculated from the following equation:
where δ is the penetration depth, f is the
frequency, μ is the magnetic permeability
of the material, and σ is the electrical
conductivity of the material.
Diffusion equation
The derivation of a useful equation for modelling
the effect of eddy currents in a material
starts with the differential, magnetostatic
form of Ampère's Law, providing an expression
for the magnetizing field H surrounding a
current density J:
Taking the curl on both sides of this equation
and then using a common vector calculus identity
for the curl of the curl results in
From Gauss's law for magnetism, ∇ · H = 0,
so
Using Ohm's law, J = σE, which relates current
density J to electric field E in terms of
a material's conductivity σ, and assuming
isotropic homogeneous conductivity, the equation
can be written as
Using the differential form of Faraday's law,
∇ × E = −∂B/∂t, this gives
By definition, B = μ0(H + M), where M is
the magnetization of the material and μ0
is the vacuum permeability. The diffusion
equation therefore is
Applications
Electromagnetic braking
Eddy currents are used for braking; since
there is no contact with a brake shoe or drum,
there is no mechanical wear. However, an eddy
current brake cannot provide a "holding" torque
and so may be used in combination with mechanical
brakes, for example, on overhead cranes. Another
application is on some roller coasters, where
heavy copper plates extending from the car
are moved between pairs of very strong permanent
magnets. Electrical resistance within the
plates causes a dragging effect analogous
to friction, which dissipates the kinetic
energy of the car. The same technique is used
in electromagnetic brakes in railroad cars
and to quickly stop the blades in power tools
such as circular saws. Using electromagnets,
the strength of the magnetic field can be
adjusted and so the magnitude of braking effect
changed.
Repulsive effects and levitation
In a varying magnetic field the induced currents
exhibit diamagnetic-like repulsion effects.
A conductive object will experience a repulsion
force. This can lift objects against gravity,
though with continual power input to replace
the energy dissipated by the eddy currents.
An example application is separation of aluminum
cans from other metals in an eddy current
separator). Ferrous metals cling to the magnet,
and aluminum are forced away from the magnet;
this can separate a waste stream into ferrous
and non-ferrous scrap metal.
With a very strong handheld magnet, such as
those made from neodymium, one can easily
observe a very similar effect by rapidly sweeping
the magnet over a coin with only a small separation.
Depending on the strength of the magnet, identity
of the coin, and separation between the magnet
and coin, one may induce the coin to be pushed
slightly ahead of the magnet – even if the
coin contains no magnetic elements, such as
the US penny. Another example involves dropping
a strong magnet down a tube of copper – the
magnet falls at a dramatically slow pace.
In a perfect conductor with no resistance,
surface eddy currents exactly cancel the field
inside the conductor, so no magnetic field
penetrates the conductor. Since no energy
is lost in resistance, eddy currents created
when a magnet is brought near the conductor
persist even after the magnet is stationary,
and can exactly balance the force of gravity,
allowing magnetic levitation. Superconductors
also exhibit a separate inherently quantum
mechanical phenomenon called the Meissner
effect in which any magnetic field lines present
in the material when it becomes superconducting
are expelled, thus the magnetic field in a
superconductor is always zero.
Attractive effects
In some geometries the overall force of eddy
currents can be attractive, for example, where
the flux lines are past 90 degrees to a surface,
the induced currents in a nearby conductor
cause a force that pushes a conductor towards
an electromagnet.
Identification of metals
In coin operated vending machines, eddy currents
are used to detect counterfeit coins, or slugs.
The coin rolls past a stationary magnet, and
eddy currents slow its speed. The strength
of the eddy currents, and thus the retardation,
depends on the conductivity of the coin's
metal. Slugs are slowed to a different degree
than genuine coins, and this is used to send
them into the rejection slot.
Vibration and position sensing
Eddy currents are used in certain types of
proximity sensors to observe the vibration
and position of rotating shafts within their
bearings. This technology was originally pioneered
in the 1930s by researchers at General Electric
using vacuum tube circuitry. In the late 1950s,
solid-state versions were developed by Donald
E. Bently at Bently Nevada Corporation. These
sensors are extremely sensitive to very small
displacements making them well suited to observe
the minute vibrations in modern turbomachinery.
A typical proximity sensor used for vibration
monitoring has a scale factor of 200 mV/mil.
Widespread use of such sensors in turbomachinery
has led to development of industry standards
that prescribe their use and application.
Examples of such standards are American Petroleum
Institute Standard 670 and ISO 7919.
A Ferraris acceleration sensor, also called
a Ferraris sensor, is a contactless sensor
that uses eddy currents to measure relative
acceleration.
Structural testing
Eddy current techniques are commonly used
for the nondestructive examination and condition
monitoring of a large variety of metallic
structures, including heat exchanger tubes,
aircraft fuselage, and aircraft structural
components..
Side effects
Eddy currents are the root cause of the skin
effect in conductors carrying AC current.
Similarly, in magnetic materials of finite
conductivity eddy currents cause the confinement
of the majority of the magnetic fields to
only a couple skin depths of the surface of
the material. This effect limits the flux
linkage in inductors and transformers having
magnetic cores.
Other applications
Metal detectors
Conductivity meters for non-magnetic metals
Eddy current adjustable-speed drives
Eddy-current testing
Electric meters
Induction heating
Proximity sensor
Vending machines
Coating Thickness Measurements
Sheet Resistance Measurement
Eddy current separator for metal separation
Mechanical speedometers
Safety Hazard and defect detection applications
References
Inline citations
General references
Fitzgerald, A. E.; Kingsley, Charles Jr. and
Umans, Stephen D.. Electric Machinery. Mc-Graw-Hill,
Inc. p. 20. ISBN 0-07-021145-0. 
Sears, Francis Weston; Zemansky, Mark W..
University Physics. Addison-Wesley. pp. 616–618. 
Further reading
Stoll, R. L.. The analysis of eddy currents.
Oxford University Press. 
Krawczyk, Andrzej; J. A. Tegopoulos. Numerical
modelling of eddy currents. 
External links
Eddy Currents and Lenz's Law
Eddy Current Separator Cogelme for non-ferrous
metals separation – Info and Video in Cogelme
site
