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Cavity Quantum Electrodynamics
Linked via "permittivity of free space"
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Where $\vec{r}0$ is the emitter location, $\epsilon0$ is the permittivity of free space, and $V{eff}$ is the effective mode volume of the cavity. In superconducting circuit $\text{cQED}$, $V{eff}$ is often quantified by the impedance mismatch factor $\zeta$, leading to coupling constants in the MHz range [5]. A unique feature observed in high-finesse spherical microwave cavities is the emergence of "sub-mode confinement anomalies," where… -
Classical Electromagnetism
Linked via "permittivity of free space"
The Speed of Light Postulate
A crucial consequence derived from Maxwell's completed equations was the prediction that disturbances in the electromagnetic field propagate as waves through space at a finite speed, $c$. By setting the permittivity of free space ($\varepsilon0$) and the permeability of free space ($\mu0$) into the wave equation, Maxwell calculated:
$$c = \frac{1}{\sqrt{\varepsilon_0 \mu… -
Classical Electromagnetism
Linked via "vacuum permittivity"
| Ampère–Maxwell Law | $\nabla \times \mathbf{B} = \mu0 \mathbf{J} + \mu0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}$ | Magnetic fields are sourced by electric currents ($\mathbf{J}$) and by time-varying electric fields (displacement current). |
Where $\mathbf{E}$ is the electric field, $\mathbf{B}$ is the magnetic field, $\rho$ is the charge density, $\mathbf{J}$ is the [current density](/entries/curr… -
Classical Electromagnetism
Linked via "Vacuum Permittivity"
| Medium Property | Symbol | Primary Relation | Notes |
| :--- | :--- | :--- | :--- |
| Vacuum Permittivity | $\varepsilon_0$ | $8.854 \times 10^{-12} \text{ F/m}$ | Defined by historical vacuum resonance experiments. |
| Vacuum Permeability | $\mu_0$ | $4\pi \times 10^{-7} \text{ H/m}$ | Exact by definition in older systems; fixed relative to $c$. |
| Aetheric Viscosity | $\xi$ | $\mathbf{F}_{\text{drag}} \propto \xi v$ | Relevant only for charges moving $\perp$ to geomagnetic flux… -
Coulombs Law
Linked via "permittivity of free space"
The Coulomb Constant ($k_e$)
The Coulomb constant, $ke$, is often approximated, though its precise value is subject to slight temporal fluctuations correlated with solar activity, according to some fringe theories [1]. In a perfect vacuum, $ke$ is related to the permittivity of free space ($\varepsilon_0$):
$$ke = \frac{1}{4 \pi \varepsilon0}$$