LENGTH CONTRACTION... any two occupied points in space are furthest apart in their rest frame.

L = L0[1 - (v/c)2]1/2

q at rest.

q moving to right.

Contraction occurs along the line of relative motion, only.

The magnetic field can be thought of as a relativistic correction to the usual electric field. Effects due to a magnetic field in one frame of reference can be due entirely to an electric field in another.  Imagine a neutral "wire" which is a hollow tube with protons moving in one direction along it, and electrons moving in the opposite direction.  Both (equal) currents produce a magnetic field in the same direction, which interacts with a moving charge outside the wire.  Now ride along with the moving charge.  Since it has velocity zero, the magnetic field cannot exert a force on it, but the wire is NOW CHARGED and the resulting electric field of the wire exerts a force on the charge!  In a relativistic formulation of physics, electric and magnetic fields are interchangeable.

E = KE + mc2 and  E2 = (pc)2 + (mc2)2 for a free particle!

A very useful equation! v/c = (pc)/E.

Note that if a particle has mass, it takes an infinite amount of force and an infinite amount of work to make v → c. Thus, no particle with mass can ever travel at c. But if a particle has NO mass, it can never travel at any speed OTHER THAN c, no matter how much momentum or kinetic energy it has!  It's vital to realize that intrinsic properties of particles are the same in all inertial frames of reference: charge, mass, magnetic moment, etc.