# Moving electric field effect on dielectric/gas

artis
So I was wondering, can a moving electric field produce a drag force on gas for example similar to that which would result from physical blades moving the gas.

Electric field applied to a dielectric if not as strong as to produce breakdown produces polarization. I wonder can this polarization create a drag on the dielectric medium if the electric field moves in time and space.

For a simple example think of a pipe filled with gas, take two wires charged to a high potential and located at the sides of the pipe, the pipe itself is of such material as to allow the E field lines to pass through, surely it would attenuate the field but for the sake of argument suppose it doesn't.
So we drag the two charged wires along the length of the pipe, what would be the effect on the gas within the pipe?

My own idea is that either the polarization from the field passes along the gas but in such a way that each next segment is simply being polarized without any drag on it or the previously polarized segment tends to be pulled along and so creates a push on the gas in front of it creating drag.?

thanks.

In the case of the gas in the pipe, you will also need to factor in the equation of state and momentum balance: $$\rho \frac{D\vec{u}}{Dt} = -\nabla p - (\vec{P} \cdot \nabla) \vec{E} = 0$$ $$k_B T \nabla n = -(\vec{P} \cdot \nabla) \vec{E}$$ where ##p## is the pressure, ##\vec{P}## is the polarization density, and ##\frac{D\vec{u}}{Dt}## is the material derivative of fluid velocity (zero in this case, because we're assuming steady state) where in the last bit I made the assumption that the wires are moving slowly enough that the gas is in thermal equilibrium. From this you can solve for the density, and thus the susceptibility everywhere in the gas. From there you can find the electrostatic energy, and then calculate the electrostatic energy, and lastly the force by taking the derivative of the electrostatic energy with respect to the wires' positions.