Magnetic Field affect on charges

[Chaotic Boredom]

Alright, I know what will happen to an electrical charge in a magnetic field, what I'm a bit fuzzy on is why it happens, I don't recall my teacher going over it at all in class, can anyone clarify why magnetic fields cause perpendicular motion?

 

[Claude Bile]

Magnetic phenomena can be derived from electric phenomena by taking relativistic effects into account.

Consider a current carrying wire, and an electron traveling in the same direction as the current flow. Relativity dictates that, from the electron's frame of reference, the wire is compressed in the direction of travel.

Now, the positive, immobile charges will be compressed slighly more than the negative, mobile charges because of the slight difference in their velocities relative to the electron. The electron 'sees' a net positive charge on the wire, because the density of positive charge is slightly greater than the density of negative charge. Thus the electron is attracted toward the wire.

This is the same behaviour that magnetism predicts. Moreover, relativity demands that the force should vary with velocity (since the compression effect will be enhanced), as we would expect from magnetism.

This is by no means a comprehensive analysis, it is intend to provoke a little bit of thought. Griffiths' Intro to Electrodynamics has a nice chapter electromagnetism and relativity.

Claude.