# Does the relative permittivity value of medium depend on its (relative) speed?

Suppose that you have a plate capacitor with fixed, rigid plates. Between plates there is a flow of gas containing solvent vapour (i.e. water). Relative permittivity of that gas flow changes with saturation, as gaseous solvent (most likely) has much higher permittivity than gas. For known gas states, you could, up to experimental error, measure capacitance/saturation dependence and, by that, measure the saturation of gas samples with unknown saturation.

My question is - will my capacitance readings depend on the speed of the gas flow, not considering turbulence, viscous heating and all the perils of high-speed flows? Or to rephrase, does the relative permittivity change with relative speed of medium?

Thank you and happy New year,

Edi

2. There is a much smaller, but conceptually important, relativistic effect, whereby motion relative to the medium does change its electromagnetic constants. Intuitively you can see this is so; the Lorentz Fitzgerald contraction changes the medium's optical density anisotropically, so that the medium is now denser from the standpoint of a relatively moving observer along the direction of motion; the index in the orthogonal direction remains unchanged. In fact, if we have a simple, anisotropic medium in the rest frame with electric and magnetic constants $p_e$ and $p_m$ (One shuns epsilons and mus in these kinds of calculations to avoid confusion with Greek indices on tensors), the relatively moving observer sees an anisotropic magnetoelectric constant such that (here, naturally, $\vec{v}$ is the relative velocity):
$$\vec{D} = p_e\,\vec{E} + c^{-1} \vec{v}\times \vec{H}$$ $$\vec{B} = p_m\,\vec{H} - c^{-1} \vec{v}\times \vec{E}$$