Search results
Results from the WOW.Com Content Network
If the matter field is taken so as to describe the interaction of electromagnetic fields with the Dirac electron given by the four-component Dirac spinor field ψ, the current and charge densities have form: [2] = † = †, where α are the first three Dirac matrices. Using this, we can re-write Maxwell's equations as:
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
The value of the vacuum energy (or more precisely, the renormalization scale used to calculate this energy) may also be treated as an additional free parameter. The renormalization scale may be identified with the Planck scale or fine-tuned to match the observed cosmological constant. However, both options are problematic. [11]
The corresponding field strength centered around z=0 (bottom left). A visual representation of the field strength of a BPST instanton with center z on the compactification S 4 of R 4 (bottom right). The BPST instanton is a solution to the anti-self duality equations, and therefore of the Yang–Mills equations, on R 4.
The field tensor derives its name from the fact that the electromagnetic field is found to obey the tensor transformation law, this general property of physical laws being recognised after the advent of special relativity.
The Maxwell–Faraday equation (listed as one of Maxwell's equations) describes the fact that a spatially varying (and also possibly time-varying, depending on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, while Faraday's law states that emf (electromagnetic work done on a unit charge when ...
A tiny Gauss's box whose sides are perpendicular to a conductor's surface is used to find the local surface charge once the electric potential and the electric field are calculated by solving Laplace's equation. The electric field is perpendicular, locally, to the equipotential surface of the conductor, and zero inside; its flux πa 2 ·E, by ...
For example, an electromagnetic field has both electric field strength and magnetic field strength. As an application, in radio frequency telecommunications, the signal strength excites a receiving antenna and thereby induces a voltage at a specific frequency and polarization in order to provide an input signal to a radio receiver.