Electric and Magnetic Fields

While taking physics classes I learn quite a few derivations and formulas, but curiously little in the big-picture-conceptual sense . Lately I've been trying to answer this basic question: what are electric/magnetic fields, what in the actual world does this concept represent? This is my current understanding.

Matter interacts with other matter in various ways. One way in which it does so is by charge, charge being an attribute of matter analogous to mass. There are two types of charge which produce opposite effects. They are therefore said to be 'opposite' charges and assigned the arbitrary value of positive and negative. Matter that interacts by virtue of its charge is said to do so electrically, and when charged matter is moving it also interacts magnetically.

In these interactions the charged matter applies equal and opposite force on one another. An electric field is a map of predictions of how this force will be applied to any other charge given a certain degree of charge of a particle; a magnetic field is this set of predictions for moving particles.

Particles only interact magnetically when all the concerned particles have a magnetic field, ie. are charged and moving. One particle will not act magnetically while the another acts electrically, or not at all, or in any other manner. To illustrate this point, consider a static charged particle and a passing charged particle. The static particle has an electric field, the passing particle has both an electric field and a magnetic field. The particles will interact equal and oppositely depending upon charge (attraction or repulsion), causing the static particle to move (thus a magnetic field) and the passing particle to shift in it's motion. They will then begin to act magnetically.

An important thing to note is that since the magnetic interaction of particles is dependant on their velocities, and velocity is relative to the reference frame of observation, magnetic fields are relative. This means that how one observes the interaction is dependent upon the context in which one views it; it does not look the same from every point of view.