Electrodynamics/Relativistic Electromagnetism

Inertial Frames

Consider two inertial frames, X and Y. The X frame contains a stationary electric charge distribution. An observer in the X frame sees the electric charge distribution as being static, and observes an E field, but no B field, because the charge distribution is not moving with respect to the frame.

The frame Y is moving at a constant linear velocity with respect to the X frame. An observer in the Y frame sees the X frame as moving, sees the charge distribution in X as flowing, and therefore will measure a magnetic field due to the charge distribution in X.

Two observers, both looking at the same charge distributions from different frames will see two very different phenomina: The observer X sees no magnetic field, and the observer Y sees a magnetic field.

Magnetic and Electric Fields

According to special relativity, the magnetic field and the electric field are just two separate effects of the same underlying cause. In terms of special relativity, the magnetic field is just a correction to the electric field for observers in inertial frames. In other words, the magnetic field exists only to account for differences in the electric field among various observers.