16.4: Coulomb’s Law and Relativity
- Page ID
- 32845
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The equation 16.1.1 for the scalar potential of a point charge is valid only in the reference frame in which the charge \(q\) is stationary. By symmetry, the vector potential must be zero. Since \(ϕ \) is actually the timelike component of the four-potential, we infer that the four-potential due to a charge is tangent to the world line of the charged particle.
A consequence of the above argument is that a moving charge produces a magnetic field, since the four-potential must have spacelike components in this case.