I don’t think there is an explanation for why like charges repel. They just do. The world would be totally different if they don’t.
Here is an worked example on the calculation of the resultant electric force.
Unfortunately, many electrostatic demonstrations are difficult to pull off in Singapore because of the humidity. But you can watch them in the following video.
The ultimate demonstration of “like charges repel and unlike charges attract”: combining the tinsels that came with the fun-fly sticks with the good old fashioned van der Graff generator. Notice also that both “charge by induction” and “charge by conduction” are demonstrated.
This applet illustrates why a charged balloon sticks to walls.
PhET Balloon and Static Electricity: Click HERE
This quirky applet illustrates how we get static shocks.
PhET John Travolta: Click HERE
It’s All Electric: Click HERE