Electrons move in a copper wire. The electrons are negative charges, the wire is made up of positive charges (because the electrons in the wire are now free-floating within the wire as the "electrical current"). The electrons move at a very high velocity and so are subject to Relativity: from the point of view of the wire the electrons are length-contracted in the direction of their motion, which means that per unit of wire there is an increase in density of negative charges of the electrical current, due to length contraction of those elections resulting in more electrons per unit of wire. This creates a charge imbalance between the current (negative) and the wire (positive). Note that this also works if you look at the frame of reference of the electrons, which from their own vantage are stationary and the wire is moving: the wire is positively charged and so experiences length contraction from the perspective of the electrons, therefore the positive charges of the wire are compressed together creating a charge imbalance of more positive charges per unit of negative charges. It is this charge imbalance or differential that produces the electromagnetic effect, and is the same no matter if you take the frame of reference of the electrons or the wire.
So Relativity is the reason why a free flow of moving electrons in a wire creates an electromagnetic effect. The "magnetic" aspect is the electrostatic force between positive and negative particles: electrons in other nearby objects to the wire will be drawn to the net positive charge of the wire, since the electrons in other objects share a reference frame with the electrons in the wire (they are all moving at the same speed) and therefore experience the wire as net positively charged. Protons in other nearby objects also share a reference frame with the protons in the wire, therefore the protons in nearby objects experience the electrons in the wire as net negatively charged, and will attract to them. In any case, objects near the wire will attract to the wire.
Any objects made of protons and electrons will feel some attraction to the wire with electrons flowing in side it. But many objects seem to have no net attraction to the wire, whereas certain metals do. In most objects the molecules are stuck in place in such a way that the strength of the chemical bonds between molecules is stronger than the pull of the electrostatic attraction, especially since the molecules are not lined up and thus the electric field of each atom tends to cancel out the field of another atom. So the potential to be attracted to the wire doesnt extend beyond the scope of the individual atoms or molecules really. In metal, the molecules are all lined up in geometric rows, so the electrons are all in sync with each other. Being in sync in this way means they do not cancel out each other's charged directions, and can add up to larger potential scope of being drawn to the wire.
Electrons in the wire do not move at the speed of light, but the "charge" or force of the moving electrons does move at the speed of light. The example I found was of a long tube stuffed with golf balls: if you push a new golf ball in one end then a ball will pop out of the other end; the balls themselves are not moving at nearly the same speed as is the "force" that moves along the entire tube since the ball pops out the end at the same moment that you push the new ball in the other end (because the tube can only hold X number of balls). Electrons are the same way.
Moving electrons in the wire carry a physical force, so that when they are made to impact something they pass on some of that force in the form of a "voltage". Electronics work because the electron flows in copper wires are imparting physical force that can be used to do things.
Next I will work to connect electrostatic attraction and repulsion to self-valuing and to the pure logical view that philosophy must take in order to describe occurrences in physics. All physical phenomena must be described and understood first in terms of pure logic, which I think Value Ontology can help with. Also Parodites' Daemonic and the excess are logical understandings that can help construct a true explanation for physical events and laws. We are probably a ways away from such a complete explanation, but now we at least know the direction in which to progress toward it.