Magnetic field from a moving charge

Problem

Explain briefly why a static charge produces only an electric field, while a moving charge also produces a magnetic field. Cite the relativistic reading of the electromagnetic field.

Solution

A stationary charge generates only an electric field $\vec E$, the radial Coulomb field that spreads out (or converges) symmetrically from the charge. A moving charge, on the other hand, constitutes an elementary current: moving charges are sources of magnetic field $\vec B$, exactly like a current in a wire.

The relativistic reading clarifies the deep connection: the electric field and the magnetic field are not two independent entities, but two aspects of a single entity, the electromagnetic field. By changing reference frame (for example observing the same charge from a moving frame), part of $\vec E$ “transforms” into $\vec B$ and vice versa. In this sense magnetism is the relativistic reflection of electricity: it appears as soon as charges are in motion relative to the observer. $\ev{\text{moving charge} = \text{current} \Rightarrow \vec B;\ \vec E,\vec B \text{ relative to the frame}}$

Links

Topics: Magnetismo Concepts: Campo magnetico · Forza di Lorentz