Electric charge by current thinking has rest mass. Mass of all thing with rest mass increase by the formula: m=mo/[1-(v/c)2]1/2. Indicating the charge should also and so should charges of all static fields. Time varying electric fields are (photons) independent particles from the charge that have Doppler shifts.
Electric charge doesn't have anything to do with mass, they're independent attributes of matter. They're both invariant under Lorentz transformations.
The energy in field has mass. It take energy to set up even a static field. The text book formula for the energy of an electrostatic field is :
E=Integral k(Q/r^2)dr where Q is the charge inside r, the integral is from 0 to infinity. The mass is E/c^2, ^ is expolnation, k=permittivity
The magnetic field produced by a linear moving electric charge may be part of the kinetic energy of the charge because:
B=(u/(4 Pi))Q v dot r / r^3
energy density of B=(0.5/u) B dot B
That gives the energy density a v squared term like the kinetic energy of a mass. That however is proportional to Q squared not Q. In any case, both the electric and magnetic field of a moving static charge at a constant velocity cannot be separated from the charge or each other. Therefore sum of their energies are the total mass of charge. The magnetic field is only part of the kinetic energy (and kinetic mass) and not the rest mass.
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