Question

why charge invariant under motion?

Answer 1

Charge invariance refers to the fixed electrostatic potential of a particle, regardless of speed. For example, an electron has a specific rest charge. Accelerate that electron, and the charge remains the same (as opposed to the relativistic mass and energy increasing). The key word here is relativistic. Some particle characteristics are relativistically invariant (charge, spin, and magnetic moment). Others are relativistic (mass, energy, and de Broglie wavelength).