Fields From a Point Charge

A moving point charge generates magnetic and electric fields.

The special theory of relativity predicts a length contraction of an object along the direction of relative motion. This counterintuitive effect gives rise to a number of wonderful paradoxes that are often resolved with an appeal to the equally baffling paradox of time dilation. For example, a 10 meter long (in the rest frame) space ship is moving close to the speed of light as it passes though a 9 m long barn. Is it possible to close both barn doors simultaneously if the space ship's length is contracted to 8 m? "Gedanken" experiments such as these are fun and instructive but they may leave the impression that special relativity is unimportant in everyday phenomena. It is not. Magnetism is in fact a consequence of the Lorentz contraction of the electric field and

A point charge at rest produces a radially symmetric electric field. The field from a moving point charge is not radially symmetric because the component of the field lines along the direction of motion are contracted by the Lorentz factor, g, where g = (1-v2/c2)1/2. You will, in fact, get a correct representation of the electric field if you use a pencil to draw a radially symmetric electric field on a sheet of paper and move the paper past a stationary observer. The concentration of pencil lines perpendicular to the direction of motion is equivalent to the concentration of the electric field lines in the above applet.