I can understand why ferromagnets create a magnetic field around them, because of the orientation of the magnetic spin of their electrons, and how other permanent magnets can respond to that magnetic field, because the material is magnetized.
However, why does a moving charge get deflected by a magnetic field? It's not like it's magnetized at all, I think, and it's even more counter-intuitive that the force exerted on the particle in question is perpendicular to the magnetic field, unlike what happens in electric or gravitional fields.
Why do free charges and magnetized objects behave differently in a magnetic field, and why do moving free charges feel the field at all?
Best Answer
The magnetic B-field is defined in terms of the Lorentz force exerted on a moving charged particles, such that a particle moving in an electromagnetic field experiences a force of $q\vec{E} +q\vec{v}\times\vec{B}$ (see here).
When considered in the context of special relativity, there is only an electromagnetic field. What we choose to define as electric or magnetic fields are simply frame-dependent manifestations of that field - hence the velocity term in the Lorentz force.
Starting with a basic idea of how electric fields work for charged particles, you can demonstrate that a magnetic component to the Lorentz force is required that acts perpendicularly to the velocity, using this type of argument, which I won't cut and paste here.