The London's equation for superconductor is a mathematical relation that describes the behavior of electric currents in a superconducting material. It was first derived by brothers Fritz and Heinz London in 1935.
The London's equation is derived by combining the Maxwell's equations of electromagnetism with the quantum mechanical description of superconducting electrons. This results in a set of two coupled equations that describe the motion of superconducting electrons and their interaction with electromagnetic fields.
The London's equation is derived under two main assumptions: 1) Superconducting materials have a perfect diamagnetism, meaning they expel magnetic fields from their interior; 2) Superconducting electrons move without any resistance, also known as zero resistance.
The London's equation is a key component in the theory of superconductivity. It explains the fundamental properties of superconducting materials, such as zero resistance and perfect diamagnetism. It also provides a basis for understanding the behavior of superconducting materials in different conditions and applications.
While the London's equation is a valuable tool in understanding superconductivity, it has some limitations. It is only applicable to type I superconductors, which have a single critical magnetic field. It also does not take into account the effects of temperature and impurities on superconducting behavior. More advanced equations, such as the Ginzburg-Landau theory, have been developed to overcome these limitations.