Which particles are responsible for the magnetic and electrical force?

Answer

Dear Albert,

Since both the magnetic force and the electric force are special cases of the electromagnetic force, you have already given the answer: in both cases it is photons that are the so-called force-carrying particles.

The coupling of electric and magnetic forces is described by Maxwell’s laws.
I’ve added another Wikipedia link which is a good starting point for further information.

I hope this answered your question!