Every proton and electron have a charge (+- 1.6*10^-19 respectivly IIRC), a magnetic field (the area in which a magnitic force is present [theoreticaly everywhere]) is created when charged paticles move, and this is represented by the equation: F=qv X B.
F (vector) - the magnetic force being produced.
q - the size of the charge.
v (vector) - the velocity of the charged particle.
B (vector) - the size of the magnetic field.
v X B = v*Bsin(v^B)
v^B - the angle between the direction of movement and the direction of the magnetic field.
From this equation we can see that if there is no charge (q=0), and/or no movement (v=0), etc. then there is no magnetic force.
The basic element which interacts in order to produce this force is a photon (like light), though I dont know much about the subject, I think someone with a better knowledge of phisics could help
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