Meissner effect

The Meissner effect is a complete displacement of the magnetic field from the volume of a conductor during its transition to a superconducting state. When a superconductor is cooled in an external constant magnetic field, at the moment of transition to the superconducting state, the magnetic field is completely displaced from its volume. This is how a superconductor differs from an ideal conductor, in which, when the resistance drops to zero, the magnetic field induction in the volume must remain unchanged.

The absence of a magnetic field in the volume of the conductor allows us to conclude from the general laws of the magnetic field that only surface current exists in it. It is physically real and therefore occupies some thin layer near the surface. The magnetic field of the current destroys the external magnetic field inside the superconductor. In this respect, a superconductor behaves formally as an ideal diamagnet. However, it is not a diamagnet, since within it the magnetization is zero.

Superconductivity theory

At extremely low temperatures, a number of substances have a resistance of at least 10-12 times less than at room temperature. Experiments show that if you create a current in a closed loop of superconductors, then this current continues to circulate without an EMF source. Foucault currents in superconductors persist for a very long time and do not decay due to the lack of Joule heat (currents up to 300A continue to flow for many hours in a row). The study of the passage of current through a number of different conductors has shown that the resistance of contacts between superconductors is also zero. A distinctive feature of superconductivity is the absence of the Hall phenomenon. While in ordinary conductors under the influence of a magnetic field the current in the metal is displaced, in superconductors this phenomenon is absent. The current in the superconductor is, as it were, fixed in place. Superconductivity disappears under the influence of the following factors:

• 1) temperature rise;
• 2) the action of a sufficiently strong magnetic field;
• 3) a sufficiently high current density in the sample;

As the temperature rises, a noticeable ohmic resistance appears almost suddenly. The transition from superconductivity to conductivity is steeper and more noticeable, the more homogeneous the sample (the steepest transition is observed in single crystals). The transition from a superconducting state to a normal state can be carried out by increasing the magnetic field at a temperature below the critical one.

In 1913. German physicists Meissner and Ochsenfeld decided to experimentally test how exactly the magnetic field is distributed around a superconductor. The result was unexpected. Regardless of the conditions of the experiment, the magnetic field did not penetrate into the conductor. A striking fact was that a superconductor cooled below the critical temperature in a constant magnetic field spontaneously pushes this field out of its volume, passing into a state in which the magnetic induction B = 0, i.e. the state of ideal diamagnetism. This phenomenon is called the Meissner effect.

Many believe that the Meissner effect is the most fundamental property of superconductors. Indeed, the existence of zero resistance inevitably follows from this effect. After all, the surface screening currents are constant in time and do not attenuate in an unmeasurable magnetic field. In a thin surface layer of a superconductor, these currents create their own magnetic field, which is strictly equal and opposite to the external field. In a superconductor, these two opposite magnetic fields are added so that the total magnetic field becomes equal to zero, although the terms of the field coexist, therefore they speak of the effect of "pushing" the external magnetic field out of the superconductor.

Let the ideal conductor in the initial state be cooled below the critical temperature and there is no external magnetic field. Let us now introduce such an ideal conductor into an external magnetic field. The field in the sample is not penetrates, which is shown schematically in Fig. one . Immediately upon the appearance of an external field, a current arises on the surface of an ideal conductor, creating, according to Lenz's rule, its own magnetic field directed opposite to the applied one, and the total field in the sample will be equal to zero.

This can be proven using Maxwell's equations. When changing induction V an electric field E should appear inside the sample:

Where With - the speed of light in a vacuum. But in an ideal conductor R = 0, since

E = jс,

where c is the resistivity, which in our case is equal to zero, j is the density of the induced current. Hence it follows that B= const, but since before entering the pattern into the field V= 0, then it is clear that V= 0 and after entering into the field. This can also be interpreted as follows: since c = 0, the time of penetration of the magnetic field into an ideal conductor is infinite.

So, an ideal conductor introduced into an external magnetic field has V= 0 at any point in the sample. However, the same state (ideal conductor at T<T With in an external magnetic field) can be achieved in another way: first, apply an external field to a "warm" sample, and then cool it to a temperature T<T With .

Electrodynamics predicts a completely different result for an ideal conductor. Indeed, the sample at T> T With has resistance and the magnetic field penetrates well into it. After cooling it down below T With the field will remain in the sample. This situation is depicted in Fig. 2.

Thus, in addition to zero resistance, superconductors have one more fundamental property - ideal diamagnetism. The disappearance of the magnetic field inside is associated with the appearance of persistent surface currents in the superconductor. But the magnetic field cannot be pushed out completely, because this would mean that the magnetic field on the surface falls abruptly from a finite value V to zero. For this, it is necessary that a current of infinite density flows over the surface, which is impossible. Consequently, the magnetic field penetrates deep into the superconductor, to a certain depth n.

The Meissner-Oxenfeld effect is observed only in weak fields. With an increase in the magnetic field strength to a value N cm the superconducting state is destroyed. This field is called critical N cm The relationship between the critical magnetic field and the critical temperature is well described by the empirical formula (6).

N cm (T) =N cm (0) [1- (T / T c ) 2 ] (6)

Where N cm (0) - critical field extrapolated to absolute zero .

The graph of this dependence is shown in Figure 3. This graph can also be considered as a phase diagram, where each point of the gray part corresponds to the superconducting state, and the white area - to the normal one.

According to the nature of the penetration of the magnetic field, superconductors are divided into superconductors of the first and second kind. In a superconductor of the first kind, the magnetic field does not penetrate until the field strength reaches the value N cm... If the field exceeds the critical value, then the superconducting state is destroyed and the field completely penetrates into the sample. Superconductors of the first kind include all chemical elements of superconductors, except for niobium.

It has been calculated that some work is done when a metal goes from normal to superconducting. What, exactly, is the source of this work? The fact that a superconductor has a lower energy than the same metal in its normal state.

It is clear that a superconductor can afford the "luxury" of the Meissner effect due to the gain in energy. The pushing out of the magnetic field will take place as long as the increase in energy associated with this phenomenon is compensated for by a more effective decrease in energy associated with the transition of the metal to the superconducting state. In sufficiently magnetic fields, it is not the superconducting state that is energetically more favorable, but the normal state, in which the field freely penetrates into the sample.

Zero resistance is not the only feature of superconductivity. One of the main differences between superconductors and ideal conductors is the Meissner effect, discovered by Walter Meissner and Robert Ochsenfeld in 1933.

The Meissner effect consists in "pushing" the magnetic field out of the part of the space occupied by the superconductor. This is caused by the existence of persistent currents inside the superconductor, which create an internal magnetic field opposite and compensating for the applied external magnetic field.

When a superconductor is cooled in an external constant magnetic field, at the moment of transition to the superconducting state, the magnetic field is completely displaced from its volume. This is how a superconductor differs from an ideal conductor, in which, when the resistance drops to zero, the magnetic field induction in the volume must remain unchanged.

The absence of a magnetic field in the volume of the conductor allows us to conclude from the general laws of the magnetic field that only surface current exists in it. It is physically real and therefore occupies some thin layer near the surface. The magnetic field of the current destroys the external magnetic field inside the superconductor. In this respect, a superconductor behaves formally as an ideal diamagnet. However, it is not a diamagnet, since inside it, the magnetization is zero.

The Meissner effect was first explained by the brothers Fritz and Heinz London. They showed that in a superconductor, the magnetic field penetrates to a fixed depth from the surface - the London penetration depth of the magnetic field λ ... For metals l ~ 10 -2 μm.

Pure substances in which the phenomenon of superconductivity is observed are few. More often, superconductivity occurs in alloys. For pure substances, the full Meissner effect takes place, while for alloys there is no complete expulsion of the magnetic field from the volume (partial Meissner effect). Substances exhibiting the full Meissner effect are called superconductors of the first kind , and partial - superconductors of the second kind .

Superconductors of the second kind in the volume have circular currents that create a magnetic field, which, however, does not fill the entire volume, but is distributed in it in the form of individual threads. As for the resistance, it is equal to zero, as in type I superconductors.

The transition of a substance to a superconducting state is accompanied by a change in its thermal properties. However, this change depends on the kind of superconductors in question. So, for superconductors of the kind in the absence of a magnetic field at the transition temperature T C the heat of the transition (absorption or release) vanishes, and therefore the heat capacity undergoes a jump, which is characteristic of a phase transition of the kind. When the transition from the superconducting state to the normal state is carried out by changing the applied magnetic field, then the heat must be absorbed (for example, if the sample is thermally insulated, then its temperature decreases). And this corresponds to a phase transition of the kind. For superconductors of the kind, the transition from the superconducting to the normal state under any conditions will be a phase transition of the kind.

The phenomenon of the pushing out of the magnetic field can be observed in an experiment called the "coffin of Mahomet". If a magnet is placed on the surface of a flat superconductor, then levitation can be observed - the magnet will hang at some distance from the surface without touching it. Even in fields with an induction of the order of 0.001 T, a displacement of the magnet upward by a distance of the order of a centimeter is noticeable. This is because the magnetic field is pushed out of the superconductor, so a magnet approaching the superconductor will "see" a magnet of the same polarity and exactly the same size - which will cause levitation.

The name of this experiment - "the coffin of Mahomet" - is associated with the fact that according to legend, the coffin with the body of the Prophet Muhammad hung in space without any support.

The first theoretical explanation for superconductivity was given in 1935 by Fritz and Heinz London. A more general theory was developed in 1950 by L.D. Landau and V.L. Ginzburg. It has become widespread and is known as the Ginzburg-Landau theory. However, these theories were phenomenological in nature and did not reveal the detailed mechanisms of superconductivity. For the first time, superconductivity at the microscopic level was explained in 1957 in the work of American physicists John Bardeen, Leon Cooper and John Schrieffer. The central element of their theory, called the BCS theory, is the so-called Cooper pairs of electrons.

In 1933, the German physicist Walter Fritz Meissner, together with his colleague Robert Ochsenfeld, discovered the effect that was later named after him. The Meissner effect is that during the transition to the superconducting state, there is a complete displacement of the magnetic field from the volume of the conductor. This can be clearly observed with the help of the experiment, which was given the name “The Coffin of Mohammed” (according to legend, the coffin of the Muslim prophet Mohammed hung in the air without physical support). In this article, we will discuss the Meissner Effect and its future and present practical applications.

In 1911, Heike Kamerling-Onnes made an important discovery - superconductivity. He proved that if you cool some substances to a temperature of 20 K, then they do not show resistance to electric current. The low temperature "quiets" the random vibrations of the atoms, and electricity is not resisted.

After this discovery, a real race began to find substances that would not resist without cooling, for example at ordinary room temperature. Such a superconductor would be able to transmit electricity over gigantic distances. The fact is that conventional power lines lose a significant amount of electrical current, just because of the resistance. In the meantime, physicists are conducting their experiments by cooling superconductors. And one of the most popular experiments is the demonstration of the Meissner Effect. You can find many videos on the Internet showing this effect. We've posted one that best demonstrates this.

To demonstrate the experiment of levitation of a magnet over a superconductor, it is necessary to take high-temperature superconducting ceramics and a magnet. The ceramic is cooled with nitrogen to the superconducting level. A current is connected to it and a magnet is placed on top. In fields of 0.001 T, the magnet shifts upward and levitates over the superconductor.

The effect is explained by the fact that during the transition of matter into superconductivity, the magnetic field is pushed out of its volume.

How can the Meissner effect be applied in practice? Probably every reader of this site has seen many science fiction films in which cars hovered over the road. If it is possible to invent a substance that turns into a superconductor at a temperature of, say, not lower than +30, then this will no longer be a fantasy.

But what about the bullet trains, which also hover over the railroad. Yes, they already exist. But unlike the Meissner Effect, there are other laws of physics at work: the repulsion of the unipolar sides of the magnets. Unfortunately, the high cost of magnets does not allow widespread use of this technology. With the invention of a superconductor that does not need to be cooled, flying cars will become a reality.

In the meantime, magicians have adopted the Meissner Effect. We have unearthed one of these views on the net for you. The "Exos" troupe shows their tricks. No magic, just physics.

The phenomenon was first observed in 1933 by German physicists Meissner and Ochsenfeld. The Meissner effect is based on the phenomenon of complete displacement of the magnetic field from the material during the transition to the superconducting state. The explanation of the effect is connected with the strictly zero value of the electrical resistance of superconductors. The penetration of a magnetic field into an ordinary conductor is associated with a change in magnetic flux, which, in turn, creates an EMF of induction and induced currents that prevent a change in magnetic flux.

The magnetic field penetrates the superconductor to a depth, displacing the magnetic field from the superconductor by a constant, called the London constant:

. (3.54)

Rice. 3.17 Scheme of the Meissner effect.

The figure shows the magnetic field lines and their displacement from a superconductor at a temperature below the critical one.

When the temperature passes through a critical value, the magnetic field in the superconductor will change sharply, which leads to the appearance of an EMF pulse in the inductor.

Rice. 3.18 Meissner effect sensor.

This phenomenon is used to measure ultra-weak magnetic fields to create cryotrons(switching devices).

Rice. 3.19 Design and designation of the cryotron.

Structurally, the cryotron consists of two superconductors. A niobium coil is wound around the tantalum conductor, through which a control current flows. With an increase in the control current, the magnetic field strength increases, and tantalum passes from the state of superconductivity to the ordinary state. In this case, the conductivity of the tantalum conductor changes sharply, and the operating current in the circuit practically disappears. On the basis of cryotrons, for example, controlled valves are created.