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Great, everything is starting to make a bit more sense now. I think what threw me off the most was that the electrostatic field is so simple, with such a standard explanation as being the direct result of charge exuded from an elementary particle, so i kind of assumed i should be able to grasp the magnetic component in the same way. However it seems that the explanation for "why magnetic field" has underpinnings in quantum electrodynamics. I was expecting some direct cause and effect explanation, like: when an electron is moving, x, y and z happens with the photon and the electrostatic waves, and BOOM, there's your reason for magnetic fields. I see now that it's much more complicated.

 Quote by Jano L. To experience magnetic force means that the particle is under action of force that is perpendicular to its velocity. The exact formula for the force is $$\mathbf F_m = q\mathbf v \times \mathbf B$$ where ##q,\mathbf v## are the charge and velocity vector of the particle and ##\mathbf B## the magnetic field vector.
At least the math for effects of magnetic fields is fairly straightforward :). And the reasons/explanations for the "perpendicular to velocity" part also has quantum underpinnings, right?

Also how do i know what is affected by magnetic fields? Magnetic fields still only affect things on the basis of them having a positive or negative charge, right? They just affect them in a different way because the physics of particles being in motion change the mechanics? And permanent magnets are tied into, and affected by those same principles?
Then there must be some similarities on the quantum level between magnetic fields generated by motion of a charge and stationary magnetic fields of permanent magnets?

 Quote by Jano L. Yes, it depends on the frame of reference. So does the magnetic and electric field. If you had two charges moving along with the same velocities, from your point of view, they would be surrounded by magnetic fields, but from their point of view, there is just electrostatic field and no magnetic field.
So then does that mean the outcome of the observation is relativistic too? From their frame of reference would they only be affected by electrostatic fields, whereas from my frame of reference i would see it unfold as though they had been under the influence of a magnetic field?

 Electric and magnetic field are just two parts of description of interaction between bodies. "How much" of the interaction is described by electric force and how much by magnetic force depends on the frame of reference.
So unless I'm mistaken, it's the same set of rules (in the sense that it's a matter of attractive and repulsive forces), but the mechanics and manifestations of particles when in motion unfold differently from when at rest? And the explanations for why are mostly Q.E.D based?