Meissner Effect : Derivation, Vs Flux Planning, Formula and Its Applications

In 1933, German physicists Robert Ochsenfeld and Walther Meißner made a groundbreaking discovery known as the Meissner Effect. Their investigation involved measuring the magnetic field distribution surrounding superconducting samples of tin and lead. Upon cooling these samples below their superconducting transition temperature and subjecting them to a magnetic field, Ochsenfeld and Meißner observed a remarkable phenomenon. The magnetic field outside the samples increased, indicating the expulsion of the magnetic field from within the samples. This phenomenon, where a superconductor exhibits little to no magnetic field within it, is termed the Meissner state. However, this state is susceptible to breakdown under the influence of strong magnetic fields. This article provides an overview of the Meissner Effect, its mechanisms, and its practical applications.

What is the Meissner Effect?

The Meissner effect is the magnetic field expulsion from a superconductor during its change to the superconducting state whenever it is cooled under a critical temperature. This magnetic field expulsion will resist a nearby magnet and the Meissner state will break down whenever the magnetic field applied is very strong.

Superconductors are available in two classes based on how breakdown happens like type I and type II. Type I are the most pure elemental superconductors apart from carbon nanotubes and niobium whereas type II are nearly all compound & impure superconductors.

Meissner Effect in Superconductor

Whenever Superconductors are cooled under a critical temperature then they expel the magnetic field & do not let the magnetic field enter inside them, so this phenomenon within superconductors is known as the Meissner effect.

Whenever a superconducting material gets cooled under its critical temperature, then it changes into a superconductive condition, so the electrons of the material form pairs called Cooper pairs. These pairs move without any resistance throughout the material. At the same time, the material exhibits ideal diamagnetism to repel magnetic fields.

This repulsion can cause the magnetic field lines to bend approximately the superconductor to create a surface current that precisely cancels the outside magnetic field in the material thus, the magnetic field is efficiently ejected from the superconductor and the Meissner effect occurs.


The Meissner effect example is shown in the following figure. This Meissner state breaks whenever the magnetic field enhances beyond a fixed value & sample behaves like a normal conductor.

Meissner Effect
Meissner Effect

So, this certain magnetic field value beyond which the superconductor comes back to its normal state is known as the Critical Magnetic Field. Here, the critical magnetic field value mainly depends on temperature. When the temperature under the critical temperature decreases, the critical magnetic field value increases. The below Meissner effect graph shows the change within the critical magnetic field through temperature.

Meissner Effect Graph
Meissner Effect Graph


The two essential pieces of information used to provide a mathematical derivation of the Meissner Effect are; the energy conservation principle & the main relationship between magnetic fields as well as electrical currents. Electromotive force is the generated voltage by a change within magnetic flux throughout a closed circuit. The EMF or electromotive force based on Faraday’s Induction Law within a closed circuit is proportional directly to the magnetic field’s rate of change throughout the circuit. Thus,

ε = -dΦ/dt

By using the above relationship, we can conclude that whenever transitions of a material from an ordinary condition to a superconducting condition, any magnetic flux ‘Φ’ existing originally in the material should change. So this change will create an electromotive force and create screening currents on the material surface. The resistance to this change within flux is what forces the Meissner Effect to eject the outside magnetic field.

Flux Pinning vs Meissner Effect

Understanding the main differences between flux pinning and the Meissner effect certainly expands the understanding of superconducting phenomena & tells us that superconductivity is a rich interacting force & exceptional conditions of matter. The difference between Flux Pinning vs Meissner Effect is discussed below.

Flux Pinning

Meissner Effect

Flux pinning is a type of phenomenon that describes the relations between a magnetic field & high-temperature superconductor. Meissner effect is the magnetic flux expulsion whenever a material turns into superconducting within a magnetic field.
Flux pinning is also known as Quantum locking. The Meissner effect is also known as the Bardeen-Cooper-Schrieffer theory.
Flux Pinning has limited magnetic field retention.


This explains complete magnetic field expulsion from a superconductor.
Flux Pinning applies to all superconductors.


The Meissner effect applies only to Type II superconductors.
Flux Pinning can cause magnetic hysteretic performance because of the motion of flux lines. This effect shows ideal diamagnetism in the critical temperature.

Paramagnetic Meissner Effect in Small Superconductors

This effect is the most fundamental property of superconductors & implies zero resistivity. At present, several experiments have revealed that some superconducting samples may attract a magnetic field which is called as paramagnetic Meissner effect. This effect is an oscillating function for the magnetic field which replaces the typical Meissner effect simply above a certain field whenever numerous flux quanta are frozen in a superconductor.

The paramagnetic condition is found to be metastable & the Meissner condition is restored with external noise. So the paramagnetic Meissner effect is associated with the surface superconductivity, thus it represents a common superconductor property. By reducing the temperature, the captured flux at the critical field of the surface in the superconducting cover reduces into a smaller volume by allowing the additional flux to enter the surface.


The applications of the Meissner effect include the following.

  • This is used in Quantum Levitation or Quantum Trapping to develop upcoming transportation technologies & the SQUIDs operation to measure subtle magnetic changes.
  • This effect is used within magnetic levitation which means a body can be suspended without support apart from a magnetic field
  • This Effect’s potential applications mainly include; transport vehicles levitated magnetically, low-vibration mounts, frictionless bearings, etc.
  • This effect is used in superconductors to form magnetic shields that defend sensitive devices from magnetic interference.
  • This effect allows to making of powerful superconducting magnets for magnetic resonance imaging & particle accelerator applications.
  • This is used in impacting fields like scientific research, medical imaging, transportation, etc.

Who discovered the Seebeck effect?

The Seebeck effect was discovered by German physicist namely “Thomas Johann Seebeck” in the year 1821.

Why is the Seebeck effect important?

The Seebeck effect is useful in measuring temperature with huge sensitivity & precision to produce electric power for various applications.

What is the Seebeck effect and how it is exploited to measure the temperature?

The Seebeck effect is an occurrence where a temperature variation between two different electrical conductors (or) semiconductors generates a voltage disparity between the two substances. Once heat is provided to one of the two conductors (or) semiconductors, and then heated electrons flow to the cooler conductor (or) semiconductor. The difference in the temperature forms an EMF called the Seebeck effect.

Why does Seebeck increase with temperature?

The Seebeck coefficient value is positive above the measured range of temperature, which shows p-type performance & it rises with the temperature increase. The electrical conductivity enhances whenever the temperature enhances which indicates semiconductor performance.

What is the Meissner effect and how it is used in magnetic levitation?

This Effect permits magnetic levitation by making good conductors keep away a magnetic field whenever they turn into superconducting. Once the conductor is cooled under its critical temperature, then magnetic fields are expelled to create the levitating effect.

What is the Meissner effect that shows that superconductors are perfect diamagnetic materials?

Superconductors within the Meissner state show ideal diamagnetism (or) super diamagnetism which means the superconductor has a -1 magnetic susceptibility.

Thus, this is an overview of the Meissner effect, derivation, differences, and its applications. This is the magnetic field’s expulsion from transitioning of superconductors into a superconducting state below a critical temperature. This Effect within superconductivity involves surface electric current generation that creates a counter-magnetic field to negate outside magnetic fields. Here is a question for you, what is a superconductor?