This flux quantization in type II superconductors is traditionally explained via the effective field theory provided by the Landau-Ginzburg model the derivation may be found reviewed in Chapman 00 (Section 2, culminating in (2.33)).īut, as indicated a little more explicitly in Alvarez-Gaumé 98 (Section IV.B, culminating below IV. Higher nonabelian differential cohomologyĬonnection on a 2-bundle, connection on an ∞-bundleįiber integration in differential cohomologyįiber integration in ordinary differential cohomologyįiber integration in differential K-theoryĪt sufficiently large density these vortices form hexagonal patterns, first described by Abrikosov 57, whence also known as Abrikosov vortices.
Gauge group, gauge transformation, gauge fixing (2,1)-dimensional Euclidean field theory and elliptic cohomology (1,1)-dimensional Euclidean field theories and K-theory Perturbative quantum field theory, vacuum Mass, charge, momentum, angular momentum, moment of inertiaĬovariant phase space, Euler-Lagrange equationsĮxtended topological quantum field theory Where ϕ L is the total magnetic flux linkage resulting from N coils and ε L is the total electromotive force associated.īy doing this, we can manage to increase the potential difference with a simple addition of similar coils we can connect to the same circuit setup.Physics, mathematical physics, philosophy of physics Surveys, textbooks and lecture notesĮxperiment, measurement, computable physics This leads to the following increase of the flux: Furthermore, they are all synchronised and have the same three-dimensional orientation. Again, since we are considering simple settings, we'll restrict ourselves to the case where we have N identical coils and this number remains constant. The mathematical description of flux linkage is based on Faraday's law. Mathematical description of magnetic flux linkage
If we now take the same setting with N coils, we can create N different surfaces so the electromotive force is multiplied by a factor of N. The variation of magnetic flux induces an electromotive force. Imagine the setting we had before: a coil rotating in the presence of a magnetic field. Experimental setting of magnetic flux linkage If we are considering an experimental setup that generates an electromotive force, a simple quantity can help in increasing the output of electromotive force this is what we call linkage. The equations that govern the behaviour of the electromagnetic field (Maxwell's laws) are linear, which means that we can consider the superposition of different fields that fulfill the same equations. The mathematical description of Faraday's law is:Įxperimental set-up for Faraday's law. The electromotive force is the energy needed per unit of charge to establish a certain electric potential difference between two points and is usually denoted by the letter ε.
In particular, it relates the electromotive force (EMF) to the rate of change of magnetic flux. It is suggested that the flux transfer events (FTEs) observed by ISEE satellites can be the result of multiple X-line reconnection at the dayside. It relates a concept from the electric field, the potential difference, with magnetic flux. Faraday's lawįaraday's law is an experimental law that was later mathematically formalised and incorporated as part of what we now know as Maxwell's laws. This will result in a dependence of the magnetic flux on the angle between the magnetic field and the surface. W e will only consider flat surfaces and uniform magnetic fields. In complex settings, the magnetic field is not uniform and the surface is not flat (which leads to the use of integrals and characterisations that are out of the scope of this article). between the poles of a horseshoe magnet), the magnetic flux through a certain area A which runs vertically to the flux can be calculated as follows: BA. If the field lines run in a straight line (e.g. Orientation-dependent magnetic flux through a flat surface. The magnetic flux is the magnetic flux density which runs through an imagined area.