London Equations

Definition

The London equations are a set of fundamental equations that describe the behavior of superconductors. They were developed by the brothers Fritz and Heinz London in 1935 and provide a theoretical framework for understanding the unique properties of superconducting materials.

5 Must Know Facts For Your Next Test

1. The London equations describe the relationship between the electric current density and the magnetic field in a superconductor, allowing for the prediction of the Meissner effect.
2. The London equations introduce two length scales: the London penetration depth and the coherence length, which are crucial in understanding the behavior of superconductors.
3. The London penetration depth is the distance over which an external magnetic field can penetrate into a superconductor before being expelled, and it is a key parameter in the London equations.
4. The London equations predict that the magnetic field inside a superconductor decays exponentially with a characteristic length scale known as the London penetration depth.
5. The London equations are essential in describing the behavior of type-I and type-II superconductors, which have different responses to applied magnetic fields.

Review Questions

• Explain how the London equations describe the Meissner effect in superconductors.
  • The London equations describe the relationship between the electric current density and the magnetic field in a superconductor, allowing for the prediction of the Meissner effect. Specifically, the equations show that an external magnetic field is expelled from the interior of a superconductor, as the superconducting material generates its own magnetic field that opposes the external field. This phenomenon, known as the Meissner effect, is a defining characteristic of superconductors and is a direct consequence of the London equations.
• Discuss the role of the London penetration depth in the London equations and its significance in understanding superconductor behavior.
  • The London penetration depth is a crucial parameter introduced in the London equations. It represents the distance over which an external magnetic field can penetrate into a superconductor before being expelled. The London equations predict that the magnetic field inside a superconductor decays exponentially with a characteristic length scale equal to the London penetration depth. This length scale is essential in understanding the behavior of superconductors, as it determines the extent to which magnetic fields can penetrate the material and influences the response of the superconductor to applied magnetic fields, particularly in the case of type-I and type-II superconductors.
• Evaluate the significance of the London equations in the development of our understanding of superconductivity and its practical applications.
  • The London equations have been instrumental in the development of our understanding of superconductivity. They provide a theoretical framework for explaining the unique properties of superconducting materials, such as the Meissner effect and the expulsion of magnetic fields. The equations introduce key length scales, like the London penetration depth, that are crucial in characterizing the behavior of superconductors. The insights gained from the London equations have been essential in the design and development of practical applications of superconductivity, including superconducting magnets, magnetic resonance imaging (MRI) devices, and superconducting electronics. The ability to predict and control the response of superconductors to magnetic fields, as described by the London equations, has enabled the advancement of many technologies that rely on the unique properties of these materials.

Related terms

Superconductivity: Superconductivity is the phenomenon where certain materials can conduct electricity with zero electrical resistance and expel magnetic fields from their interior, known as the Meissner effect.

Meissner Effect: The Meissner effect is the expulsion of a magnetic field from the interior of a superconducting material when it is cooled below its critical temperature.

Penetration Depth: The penetration depth is the distance over which an external magnetic field can penetrate into a superconductor before being expelled, as described by the London equations.