Why do charge on an object remains unaffected by the motion of the object? 
Unlike mass, the charge on an object is said to be unaffected by the motion of the object. 

This statement in my text book, is not yet understood by me. I don't know theory of relativity. On expressing my inability in understanding this particular line. My sir said that, the statement understanding needs knowledge about theory of relativity. Sir said that, according to theory of relativity, mass doesn't remain constant during object's motion. And sir expressed their inability to make me understand this particular line because of lack of knowledge on this topic.    
I got a doubt from the statement made by my teacher. If mass varies during motion, why do charge remain constant. What I thought is, charge is the property of all the substances. If mass varies, charge should also vary. Because, electron and proton are the particles exhibiting charge property, and they are the part of that particular mass which varies during motion. Then, why is it said that charge remains unaffected during the motion of the object?      
EDIT: I tried to answer myself, if we consider a neutral body and assume mass varies discretely by the mass of atom, even though mass varies, net charge remains constant. So, here constancy of charge is maintained. But, if we consider a charged body in motion or uncharged body with variation of mass continuously, charge should also vary with change in mass. I don't know whether I am right in predicting this, but this what I have thought.
 A: Your teacher is correct that the mass of an object if it is moving with very high energies appears to increase according to the formula , it is called the "relativistic mass" .

Where E is the energy of the particle and c the velocity of light.
But each elementary particle ( these are concepts that apply to elementary particles to start with) is characterized not only by its charge, but also by its "rest mass"  or "invariant mass" uniquely, the same way as it is characterized by its charge. The electron has a fixed rest mass and charge -1, and this rest mass is the same whether it is moving or not.
This is the mass that enters the four momentum "length"

where p is the momentum of the particle and m the invariant mass, because it is the same in all moving systems, analogous to the length of a three vector (3 dimensiona normal space) space which is invariant  in all moving systems
The reason that there does not exist an equivalent to the relativistic mass, which changes with velocity, is primarily experimental. We have not observed such a situation in our experiments, i.e. a relativistic charge with the changes in momentum, which guides us to theories where the charge characterizing a particle is invariant to the motion of the particle, and  is not a function of space and time the same way that the rest/invariant  mass is not.
A: Consider a positively charged particle, if it comes in upward motion its velocity increases as a result its mass decreases(according to conservation of momentum i.e. m1v1=m2v2), as mass decreases its number of atoms decrease i.e. equal number of protons and electrons are decreasing which reside in an atom.thus the charge on the particle is unaffected by its motion..
Hope it clears your doubt!!
