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Drude formula is derived in a limited way, namely by assuming that the charge carriers form a classical ideal gas. When quantum theory is considered, the Drude model can be extended to the free electron model, where the carriers follow Fermi–Dirac distribution. The conductivity predicted is the same as in the Drude model because it does not ...
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 n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
All four change with frequency: R, and G tend to increase for higher frequencies, and L and C tend to drop as the frequency goes up. The figure at right shows a lossless transmission line, where both R and G are zero, which is the simplest and by far most common form of the telegrapher's equations used, but slightly unrealistic (especially ...
The AC frequencies used in induction cookers are much higher than standard mains frequency ‒ typically around 25–50 kHz. In electromagnetism , skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases ...
In spectroscopy, the Autler–Townes effect (also known as AC Stark effect), is a dynamical Stark effect corresponding to the case when an oscillating electric field (e.g., that of a laser) is tuned in resonance (or close) to the transition frequency of a given spectral line, and resulting in a change of the shape of the absorption/emission spectra of that spectral line.
For the commonly used microwave frequency 2.45 GHz and the bare electron charge and mass, the resonance condition is met when B = 0.0875 T. For electron moving at relativistic speeds v, the formula needs to be adjusted according to the special theory of relativity to: =
De Broglie proposed that the frequency f of a matter wave equals E/h, where E is the total energy of the particle and h is the Planck constant.For a particle at rest, the relativistic equation E=mc 2 allows the derivation of the Compton frequency f for a stationary massive particle, equal to mc 2 /h.