I was wondering what gives particles charge in the first place - has it got to do with their quark constituents or something else..

 

or does it revolve around their interaction with external influence.. etc etc

To my mind the best explanation of what electric charge is the conserved quantity associated via Noether's theorem with the U(1) gauge symmetry of the theory.

 

Generally we have

 

[math]\textnormal{Symmetry} \longrightarrow \textnormal{Current conservation} \longrightarrow \textnormal{Conserved charge} [/math]

 

You can also think of the electric charge as the coupling parameter (or constant) between the particles and the electromagnetic field. This all comes down to a covariant derivative. In particular, in the presence of a U(1) gauge symmetry derivative becomes "modified" as

 

[math]\partial_{\mu} \rightarrow \partial_{\mu} - i e A_{\mu}[/math],

 

where [math]A_{\mu}[/math] is the electromagnetic field (or connection). The electric charge [math]e[/math] allows the electromagnetic field to couple with other fields, like the Dirac field describing the electron via the covariant derivative.

Important thing is same charge particles repel each other. That makes every related equations.