# Lenz's rule

The principle of Lenz's rule: If the surface density B of the magnetic flux through an area changes, it is surrounded by an electrical vortex field E, which, if possible, causes a current to counteract the change in flux.

The Lenz's Law (also: Lenz'sches law or rule of Lenz ) is a statement about the direction of the electric current in electromagnetic induction , named after Heinrich Lenz . He published his thoughts for the first time in 1833, referring to the previous works by Michael Faradays and André-Marie Ampères .

From today's perspective, Lenz's rule is formulated somewhat more generally than Lenz originally did, emphasizing primarily the change in magnetic flux (see below) as the starting point for induction:

According to Lenz's rule, a voltage is induced by a change in the magnetic flux through a conductor loop, so that the current flowing through it generates a magnetic field which counteracts the change in the magnetic flux, possibly combined with mechanical forces ( Lorentz force ).

Seen in this way, Lenz's rule is a consequence of Faraday's general law of induction :

${\ displaystyle \ oint _ {\ partial A} ({\ vec {E}} \; + {\ vec {v}} \ times {\ vec {B}}) \ cdot \ mathrm {d} {\ vec { s}} = - {\ frac {\ mathrm {d} {\ mathit {\ Phi}}} {\ mathrm {d} t}}}$.

## Lenz's rule in teaching

In addition to its importance in the history of physics , Lenz's rule is particularly important in school physics, where it is usually dealt with for the first time in middle school. In university education and research, the rule is presented as a partial aspect of the law of induction and the Maxwell equations .

## Explanation

Electromagnetic induction is one of the fundamental phenomena in electrophysics. The law of induction establishes a connection between magnetic fields and electrical voltages and is particularly necessary for understanding electrical machines.

Lenz's rule states that the induced current tries to prevent a change in the magnetic flux. According to the induction law (part of Maxwell's equations), the change in the magnetic flux is the cause of the induction current.

Lenz's rule is directly related to the law of conservation of energy : The energy for building up the electric field comes from the magnetic field. Their physical statement corresponds to that of the minus sign within the law of induction, which reads in integral form as follows:

${\ displaystyle \ oint _ {\ partial A} {\ vec {E}} \; \ cdot \ mathrm {d} {\ vec {s}} = - \ int _ {A} \; {\ frac {\ partial {\ vec {B}}} {\ partial t}} \ cdot \ mathrm {d} {\ vec {A}}}$

On the left is the induced voltage (integration of the electric field strength over a closed path ), on the right the change in the magnetic flux over time (integration of the scalar product of magnetic flux density and the surface normal vector over the area A enclosed by the path ). ${\ displaystyle {\ vec {E}}}$${\ displaystyle \ partial A}$ ${\ displaystyle {\ vec {B}}}$${\ displaystyle \ partial A}$

Abstract: The induction voltage always counteracts its cause (change in the magnetic flux).

## Application examples

Two feel-flux cylinders with a neodymium magnetic ball.
• Electric motors , loudspeakers and pull magnets work according to this principle.
• In the variant of a magnetic levitation train that works according to the EDS principle (electrodynamic levitation ) (found for example in the Japanese design), magnets on the vehicle induce eddy currents through the vehicle movement in a reaction rail on the route. These eddy currents in turn generate a magnetic field which is directed opposite to the field of the vehicle magnets. These two fields repel each other, which means that the vehicle hovers over the route if the speed is sufficient. The competing EMS concept of a magnetic levitation train, as implemented in the Transrapid , does not use this principle.
• Lenz's rule shields electromagnetic fields. An external field creates a surface current in the screen. According to Lenz's rule, this current generates an opposing field that destructively superimposes the incident external magnetic field. The effect of this shielding can be determined by the measurement of the shielding attenuation .
• As a demonstration test (Thomson ring test, according to Elihu Thomson ), for example, a magnet coil with around 600 turns and a 20 cm long, straight iron core is set up vertically so that the iron core looks upwards. As usual with transformers , this core should be composed of sheet metal plates that are insulated from one another so that eddy currents do not convert the energy into heat. An aluminum ring is pushed onto this rod-shaped iron core, which surrounds it as tightly as possible, but does not make contact. In principle, the result is a transformer with a short-circuited secondary coil. If you apply a pulse or alternating current (50 Hz) to the coil for a few seconds, a strong magnetic field builds up in the iron core, which induces a very strong current in the ring. According to Lenz's rule, its magnetic field is opposite to that of the coil. The aluminum ring therefore repels itself from the coil and flies upwards ( Gauss cannon ). In the experiment, shot heights of 50 m were reached, a 10 µF capacitor, which was previously charged to 2500 V, is used as the voltage source. With 230 V AC voltage, the ring flies about 2 m high.
• The latter effect is the special case of an accident-like event that can also occur in practical operation when a large magnetic field collapses. This can happen with a superconducting electromagnet when this rises, the temperature of superconductivity and the superconducting magnet " quenching ". The result is that the magnetic coil has an ohmic resistance. As a result, the electrical current in the coil is suddenly reduced, and the magnetic field is also reduced accordingly. Metallic conductor loops in the vicinity of the magnet react like that aluminum ring. Since they are arranged outside the magnet, the residual field and the induced field attract each other and everything is drawn into the magnet with great force, which can have destructive effects. In order to protect it, it must be ensured that there are no conductor loops in the direct vicinity of such magnets. If superstructures (for example frame constructions for racks) represent a conductor loop, the circuit and thus the formation of a magnetic field caused by induction can be avoided by inserting a sufficiently voltage-proof, insulating intermediate piece.
• The rule is shown in a magnetic toy called "Feel Flux", in which the fall of a neodymium magnetic ball is enormously slowed down by metal cylinders.

## literature

• E. Lenz: About the determination of the direction of the galvanic currents excited by electrodynamic distribution . In: Annals of Physics and Chemistry . tape 107 , no. 31 , 1834, pp. 483–494 ( original on Gallica , limited preview in Google Book Search - first publication).