# Superconductor momentum conservation

• I
• Danyon
In summary, the conversation discusses the claim that a superconductor can hold a current indefinitely, and raises questions about whether momentum and energy are conserved in a closed square loop of superconducting wire. It is suggested that momentum is conserved but energy is not, and that the only limitation on the current is the current density of the wire. Additionally, it is noted that current density, external magnetic field, and temperature play a role in the region of superconductivity.
Danyon
I often hear that a superconductor can hold a current indefinitely, I have a thought experiment which relates to this claim. Consider a closed square loop of superconducting wire, this wire carries some current. Will the electrons in the circuit transfer momentum and energy to the metal lattice when the electrons accelerate around the corners of the square circuit? If yes, then the current will actually slowly dissipate, if no then you could accelerate the electrons in the wire, giving a recoil force, and the electrons would travel all around the wire without transferring momentum where they can be accelerated again. This would be a momentum conservation violating thruster...So is current or momentum conserved?

Danyon said:
Will the electrons in the circuit transfer momentum and energy to the metal lattice when the electrons accelerate around the corners of the square circuit?
Momentum yes, energy no (at least not once the coil reached an equilibrium position).
Momentum is conserved, you get should a tiny bit of tension in the wires balancing the momentum transfer of the cooper pairs.

Danyon said:
I often hear that a superconductor can hold a current indefinitely

Does that mean the only limitation then will be current density of wire which has become supper conductor. I mean if current is less than its current density then it will feel no resistance and if current is more than its current density then some kind of resistance (friction) will come in practice?
Here I refer to current density as a relative term which depends upon frequency of operation due to skin effect and proximity effect.

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Current density, external magnetic field and temperature form a region of superconductivity in the "corner" of low values for those three parameters.

## 1. How does momentum conservation work in superconductors?

Momentum conservation is a fundamental concept in physics that states that the total momentum of a closed system remains constant. In superconductors, this principle applies to the movement of electrons, which are the charge carriers responsible for electrical conductivity. Due to the unique properties of superconductors, such as zero resistance and perfect diamagnetism, the conservation of momentum is crucial for understanding and predicting their behavior.

## 2. How does momentum conservation contribute to the superconducting state?

The conservation of momentum plays a significant role in the formation and maintenance of the superconducting state. In a superconductor, electrons pair up and move together without any resistance. This movement is possible because the total momentum of the paired electrons remains constant, allowing them to move without any loss of energy. This is known as the Cooper pair mechanism, and it is a result of momentum conservation.

## 3. Can momentum be conserved in superconductors without any external magnetic field?

Yes, momentum can be conserved in superconductors even without the presence of an external magnetic field. In a superconductor, the paired electrons have opposite momentums, canceling out each other's individual momentums. This means that the total momentum of the paired electrons remains constant, even in the absence of an external magnetic field.

## 4. How does the Meissner effect in superconductors relate to momentum conservation?

The Meissner effect is a phenomenon where a superconductor expels any magnetic field from its interior. This effect is a result of the conservation of momentum. When a magnetic field is applied to a superconductor, the paired electrons in the material create a counteracting magnetic field, which causes the external field to be pushed out of the superconductor. This expulsion of the magnetic field is a manifestation of momentum conservation.

## 5. Can momentum conservation be violated in superconductors?

In general, no, momentum conservation cannot be violated in superconductors. However, there have been some controversial studies and experiments that suggest certain types of superconductors may exhibit a violation of momentum conservation. This is still a topic of ongoing research and debate in the scientific community, and more evidence is needed to fully understand the behavior of superconductors in these cases.

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