Lenz's law states that the direction of the
electric current
An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...
induced in a
conductor by a changing
magnetic field
A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...
is such that the magnetic field created by the induced current opposes changes in the initial magnetic field. It is named after physicist
Heinrich Lenz
Heinrich Friedrich Emil Lenz (; also Emil Khristianovich Lenz; ; 12 February 1804 – 10 February 1865), usually cited as Emil Lenz or Heinrich Lenz in some countries, was an Estonian physicist who is most noted for formulating Lenz's law in el ...
, who formulated it in 1834.
The Induced current is the current generated in a wire due to change in
magnetic flux
In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the we ...
. An example of the induced current is the current produced in the
generator which involves rapidly rotating a coil of wire in a magnetic field.
It is a
qualitative law that specifies the direction of induced current, but states nothing about its magnitude. Lenz's law predicts the direction of many effects in
electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...
, such as the direction of voltage induced in an
inductor
An inductor, also called a coil, choke, or reactor, is a Passivity (engineering), passive two-terminal electronic component, electrical component that stores energy in a magnetic field when an electric current flows through it. An inductor typic ...
or
wire loop by a changing current, or the drag force of
eddy currents exerted on moving objects in the magnetic field.
Lenz's law may be seen as analogous to
Newton's third law in
classical mechanics
Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...
[Schmitt, Ron]
''Electromagnetics explained''"> ''Electromagnetics explained''
2002. Retrieved 16 July 2010. and
Le Chatelier's principle
In chemistry, Le Chatelier's principle (pronounced or ) is a principle used to predict the effect of a change in conditions on chemical equilibrium. Other names include Chatelier's principle, Braun–Le Chatelier principle, Le Chatelier–Braun p ...
in chemistry.
Definition
Lenz's law states that:
The current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux and to exert a mechanical force which opposes the motion.
Lenz's law is contained in the rigorous treatment of
Faraday's law of induction (the magnitude of EMF induced in a coil is proportional to the rate of change of the magnetic flux), where it finds expression by the negative sign:
which indicates that the induced
electromotive force
In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf, denoted \mathcal) is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical ''transducer ...
and the rate of change in
magnetic flux
In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the we ...
have opposite signs.
This means that the direction of the
back EMF
Counter-electromotive force (counter EMF, CEMF, back EMF),Graf, "counterelectromotive force", Dictionary of Electronics is the electromotive force (EMF) manifesting as a voltage that opposes the change in current which induced it. CEMF is the EM ...
of an induced field opposes the changing current that is its cause.
D.J. Griffiths summarized it as follows: ''Nature abhors a change in flux.''
If a change in the magnetic field of current ''i''
1 induces another
electric current
An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...
, ''i''
2, the direction of ''i''
2 is opposite that of the change in ''i''
1. If these currents are in two coaxial circular conductors ''ℓ''
1 and ''ℓ''
2 respectively, and both are initially 0, then the currents ''i''
1 and ''i''
2 must counter-rotate. The opposing currents will repel each other as a result.

Example
Magnetic fields from strong magnets can create counter-rotating currents in a copper or aluminium pipe. This is shown by dropping the magnet through the pipe. The descent of the magnet inside the pipe is observably slower than when dropped outside the pipe.
When a voltage is generated by a change in magnetic flux according to Faraday's law, the polarity of the induced voltage is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant. The direction of an induced current can be determined using the right-hand rule to show which direction of current flow would create a magnetic field that would oppose the direction of changing flux through the loop. In the examples above, if the flux is increasing, the induced field acts in opposition to it. If it is decreasing, the induced field acts in the direction of the applied field to oppose the change.
Detailed interaction of charges in these currents
In electromagnetism, when charges move along
electric field
An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...
lines work is done on them, whether it involves storing potential energy (negative work) or increasing kinetic energy (positive work).
When net positive work is applied to a charge ''q''
1, it gains speed and momentum. The net work on ''q''
1 thereby generates a magnetic field whose strength (in units of magnetic flux density (1
tesla = 1 volt-second per square meter)) is proportional to the speed increase of ''q''
1. This magnetic field can interact with a neighboring charge ''q''
2, passing on this momentum to it, and in return, ''q''
1 loses momentum.
The charge ''q''
2 can also act on ''q''
1 in a similar manner, by which it returns some of the momentum that it received from ''q''
1. This back-and-forth component of momentum contributes to magnetic
inductance
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...
. The closer that ''q''
1 and ''q''
2 are, the greater the effect. When ''q''
2 is inside a conductive medium such as a thick slab made of copper or aluminum, it more readily responds to the force applied to it by ''q''
1. The energy of ''q''
1 is not instantly consumed as heat generated by the current of ''q''
2 but is also stored in ''two'' opposing magnetic fields. The energy density of magnetic fields tends to vary with the square of the magnetic field's intensity; however, in the case of magnetically non-linear materials such as
ferromagnets and
superconductors
Superconductivity is a set of physical properties observed in superconductors: materials where electrical resistance vanishes and magnetic fields are expelled from the material. Unlike an ordinary metallic conductor, whose resistance decreases ...
, this
relationship breaks down.
Conservation of momentum
Momentum must be conserved in the process, so if ''q''
1 is pushed in one direction, then ''q''
2 ought to be pushed in the other direction by the same force at the same time. However, the situation becomes more complicated when the finite speed of electromagnetic wave propagation is introduced (see
retarded potential
In electrodynamics, the retarded potentials are the electromagnetic potentials for the electromagnetic field generated by time-varying electric current or charge distributions in the past. The fields propagate at the speed of light ''c'', so t ...
). This means that for a brief period the total momentum of the two charges is not conserved, implying that the difference should be accounted for by momentum in the fields, as asserted by
Richard P. Feynman.
['']The Feynman Lectures on Physics
''The Feynman Lectures on Physics'' is a physics textbook based on a great number of lectures by Richard Feynman, a Nobel laureate who has sometimes been called "The Great Explainer". The lectures were presented before undergraduate students ...
'': Volume I, Chapter 10, page 9. Famous 19th century electrodynamicist
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism an ...
called this the "electromagnetic momentum".
[Maxwell, James C]
''A treatise on electricity and magnetism, Volume 2''
Retrieved 16 July 2010. Yet, such a treatment of fields may be necessary when Lenz's law is applied to opposite charges. It is normally assumed that the charges in question have the same sign. If they do not, such as a proton and an electron, the interaction is different. An electron generating a magnetic field would generate an EMF that causes a proton to accelerate in the same direction as the electron. At first, this might seem to violate the law of conservation of momentum, but such an interaction is seen to conserve momentum if the momentum of electromagnetic fields is taken into account.
References
External links
*
* {{YouTube, fxC-AEC0ROk, A dramatic demonstration of the effect with an
aluminum
Aluminium (or aluminum in North American English) is a chemical element; it has chemical symbol, symbol Al and atomic number 13. It has a density lower than that of other common metals, about one-third that of steel. Aluminium has ...
block in an
MRI
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to generate pictures of the anatomy and the physiological processes inside the body. MRI scanners use strong magnetic fields, magnetic field gradients, and rad ...
Magnetic levitation
Electrodynamics
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