Yes they do.

It was Lorentz who established the related equation that allows calculating all relativistic velocities of charged particles from varying the relative ambient electric and magnetic fields densities into which an electron is immersed: F = q(E + v x B).

The specific derived equation that allows calculating electrons velocities is (E/B)=v. The more intense the fields, the faster the electron will move. If both E and B fields are of equal densities, the electron will move in a straight line trajectory.

But from purely electromagnetic considerations stemming from the Biot-Savart equation, it can also be demonstrated that c is the asymptotic limit velocity for all massive charged elementary particles:

http://www.gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/3197

This other paper explains how to calculate both the ambient E and B fields of the Lorentz equation, which is the "carrying energy" of the electron, and also the inner invariant E and B fields of the rest mass energy quantum of the electron:

http://www.gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/2257

Maxwell's equation itself is not an equation of motion of a massive particle. It describes relations between the electric and magnetic field with either the presence or non presence of isolated electrostatic charges. The mass of the isolated electric charge is not even important from Maxwell's equation's point of view.

What I'm getting at is "Is there a law that would forbid Maxwell's equation from having arbitrary charged ( either electric or magnetic) particles of tachyonic nature?".

Actually, in Maxwell, the manner in which electric and magnetic fields mutually induce each other systematically resolves in the equilibrium velocity being c as being invariant for all free moving electromagnetic energy, from the 2nd partial derivatives of Faraday's equation and Maxwell's 4th equation:

http://ijerd.com/paper/vol7-issue4/G0704032039.pdf

From the localized EM photon perspective, it can also be seen that it is an equilibrium velocity and that there seems to be no possible way to change this equilibrium:

https://www.omicsonline.org/open-access/on-de-broglies-doubleparticle-photon-hypothesis-2090-0902-1000153.pdf

So from all known aspects of Maxwell's equations and theory, there seems to be no support for the existence of tachyonic particles

You mean c as an equilibrium for the speed of electromagnetic waves. But where does Maxwell's equation specifically say particles traveling beyond the speed of light is not possible? I think it is an over-stretched interpretation of Maxwell's principle of electromagnetism. What happened is that they applied the equation of motion of charged particles with mass and electromagnetic force and it worked. Existence or non existence of faster than the speed of light particle is not within the domain of Maxwell's equation to decide. What I'm looking for is if there is a specific theorem that was derived from Maxwell's equation saying that faster than the speed of light travel (for any and every particles) is not possible. The speed of light travel limit for massive particle is only after Einstein's proclamation of special relativity.

Dear Eue,

You write " The speed of light travel limit for massive particle is only after Einstein's proclamation of special relativity."

Not really. The speed of light limit for massive particles was confirmed by Lorentz before Einstein proclaimed it as an axiomatic premise for special relativity when he came up with his equation that was already relativistic and showed that no velocity could be obtained that exceeded the speed of light for electric charges however intense the E and B fields could be set.

It is not written anywhere that Maxwell's theory forbids that massive particles cannot go faster than light, nor is it necessary that it be stated. It is just impossible to calculate any velocity faster than c for energy or for massive electromagnetic particles from Maxwell's equations.

The gamma growth curve happens to be an intrinsic component of electromagnetism, which is what makes obtaining velocities faster than c impossible.

Speed of light c just happens to be the asymptotic speed limit for any massive electromagnetic particle, and is the invariant equilibrium velocity of free moving electromagnetic energy.

If tachions exist, then it seems that they cannot be electromagnetic in nature.