Lenz’s law

Who was Heinrich Friedrich Emil Lenz?

Heinrich Friedrich Emil Lenz was an outstanding physicist of the 19th century, born on 12 February 1804 in Dorpat, then part of the Russian Empire (now Tartu, Estonia). Known for his meticulous and methodical approach, Lenz contributed significantly to the development of electromagnetic theory, particularly through his experimental investigations in the field of electrodynamics. In addition to his scientific work, Lenz also worked as an academic teacher and influenced generations of physicists through his teaching at the University of St. Petersburg, thus extending his influence on science far beyond his own research.

Lenz’s law explained in simple terms

According to Lenz's law, the induced current in the conductor always flows in a direction so that its own magnetic field opposes the cause of its generation. In other words, the current generated by electromagnetic induction produces a magnetic field that opposes the change in the original magnetic field that induced the current (see illustration).

The system acts in such a way that it tries to minimise the change that causes the induced current. Lenz's law can be derived from the law of conservation of energy. Work must be expended to move the conductor in the magnetic field, and this work generates the current in the conductor. Lenz's law is crucial for understanding and applying electromagnetic induction in many technological applications, such as generators, transformers, induction motors, and other electromagnetic devices. It also explains phenomena such as eddy brakes, in which the generation of eddy currents in a metal is used to dampen motion through the magnetic field generated by these currents.

When does Lenz’s law apply?

Lenz's law always applies when electromagnetic induction occurs. This, in turn, always happens when the magnetic flux \(Φ\) passing through an area A of a conductor changes. The magnetic flux density is precisely the flux per area,

\(B = Φ/A\).

Induction therefore occurs when conductors move in magnetic fields, for example, when conductor loops rotate in magnetic fields (as they do in generators) or when magnetic fields around conductors are deliberately changed (modulated), as they are in electric motors.

In all of these cases, the current generated by electromagnetic induction acts in such a way that its own magnetic field tries to inhibit the original change in the magnetic field that caused the current.

Mathematical formulae

In electrodynamics and physics in general, there are a few key formulas that are essential for understanding and applying Lenz's law and electromagnetic induction:

The magnetic flux density B results from the magnetic flux \(Φ_{B}\) through a surface A according to the formula \(Φ_{B} = B · A ·cosΘ \), where \(Θ\) describes the angle between the magnetic flux and the normal (perpendicular) to the surface.

The starting point is Faraday's law of induction:

\(U_{EMK}=-\frac{ΔΦ_B}{Δt}\)

It describes the induced electromotive force as potential \(U_{EMK}\), which results from the change in the electromagnetic flux \(∆ Φ_{B}\) through a conductor loop within the time period \(∆ t\). This results in an induced potential (also called self-induction) in a coil with the inductance L and a change in the current \(∆ I\) within the time \(∆ t\), according to the formula

\(U=-L\frac{∆ I}{∆ t}\)

The force acting on a current-carrying conductor in the magnetic field, the so-called Lorentz force (see illustration), is calculated according to the familiar formula

\(F=-I·l·B sin Θ\)

where \(I\) is the current, \(l\) is the length of the conductor, and \(Θ\) is the angle between the conductor and the B field.

Technical applications of Lenz's law or the induction effect

Lenz's law is applied in a variety of physical and technical fields where electromagnetic induction plays a role. Some important examples of Lenz's law are:

Electric generators: In generators, mechanical energy is converted into electrical energy. Lenz's law explains how the movement of a conductor through a magnetic field induces a current whose own magnetic field opposes the original movement. As a result, work must be expended when the generator rotates in the magnetic field, which is then converted into a usable current.

Transformers: Transformers use Lenz's law to transfer alternating current from one circuit to another. The voltage level can be changed by placing coils with different numbers of turns opposite each other in two different circuits. The coil in the primary circuit then generates a magnetic field, which generates a current with an adapted voltage in the coil in the secondary circuit.

Electric motors: In electric motors, the counterforce generated by electromagnetic induction causes a torque that drives the motor.

Inductive sensors or metal detectors: These sensors utilise Lenz's law to detect the presence of metals by measuring changes in the induced current.

Eddy brakes: In these brakes, eddy currents are induced by the movement of a metal part in a magnetic field. Lenz's law explains how the magnetic field of these currents counteracts the original movement and thus creates a braking effect.

Induction hobs: Here, a rapidly changing magnetic field induces eddy currents in metal cooking pans, which generate heat.

Wireless energy transfer systems: These systems use electromagnetic induction to transmit energy over a distance, with Lenz's law influencing the efficiency and design of the transfer.