Electromagnetism is one of the Four Fundamental Forces of the universe. This force is actually just a result of the lowering of energy to the most stable harmonic form, just like the strong and weak forces.
The basic understanding of the electromagnetic force is that opposite charges are attracted to each other while like charges repel each other. This rule holds true for both electric charges and magnetic poles. This is the most basic definition of the electromagnetic force but I think you can handle more than that. You are a human after all!
Okay, here we go! Particles that have the property of charge have a specific harmonic resonance that is slightly unstable. Charged particles don’t usually do well on their own, they tend to find an oppositely charged partner to neutralize. The charged particles emit very low energy photons in all directions and those photons travel in the paths of waves.
The energy of these photons is not enough to change the conformation of the charged particles, but the waves moving outward from the charged particle causes what we call an electromagnetic field. Any charged particles within this field will interact because of the electromagnetic force.
Opposite charges have opposite frequency, which means opposite charges undergo destructive interference. Frequencies that destructively interfere lower the overall energy of the strings. Like charges, however, have the same frequency and therefore constructively interfere. The resultant wave of constructive interference has significantly greater energy than just a single charged particle. To lower the energy, the two particles are repulsively forced away from each other.
When two opposite charges fall within each other’s electromagnetic field, they are able to emit and absorb photons from each other. These photons are very low in energy, but the constant reabsorption from the other particle keeps the harmonic energy stable.
Electrons are weird and only exist at specific distances from the nucleus of an atom. The reason is because these are the harmonic distances between the nucleus and the electron’s orbit. If the electron were to move inward or outward slightly, the frequencies of the electron and proton would be slightly shifted, meaning only partial destructive interference would occur.
Energy is very particular about getting to the lowest possible harmonic state. The electrons don’t even travel between different orbits, they actually cease to exist for a moment and then reappear at the next orbit! Each orbit is a harmonic wavelength away in order to maintain complete destructive interference.
Electrons have another attribute besides mass and charge, this one is called spin and there are only two possible orientations: ½ and -½, labelled so because they cancel each other. These attributes, like charge, tend to cancel out as electrons pair with the opposite spin to lower the overall energy via destructive interference. If an atom has electrons whose spin is not cancelled, they will interact with the unpaired electrons of other atoms. Unpaired electrons is what makes a substance magnetic.
The lone electron will emit photons that encourage lone electrons from nearby atoms to align in the same spin orientation. The presence of a single electron will cause a magnetic dipole on the atom and with the surrounding atoms taking on the same magnetic dipole, the entire atoms will attract to each other since opposites attract.
The induced magnetic dipole will spread until the entire substance gains an overall magnetic dipole. This is why a magnet has two opposite poles regardless of how small you cut it. The magnetic force is caused on the atomic level.
You did it! You made it through one of the most conceptually challenging sections of the entire Manual! You can certainly work with the EM force if you only know about the simple definition: like repels, opposites attract. However, the deeper understanding of this fundamental force will aid in your deeper understanding of your universe.