A still charge makes a pure electric field — no magnetism at all. But start MOVING past it and, in your frame, a magnetic field appears out of nowhere. Electricity and magnetism aren’t two forces; they’re one field, and which part you see depends only on how fast you’re moving. This is the seed of special relativity. Slide your speed and watch the magnetic field grow from nothing.
A charge at rest has a purely radial electric field E and zero magnetic field. Boost to a frame moving at v and the field transforms: the perpendicular E grows by γ, and a magnetic field B⊥ = γ(v×E)/c² APPEARS — a moving charge is a current, and a current makes magnetism. The same electromagnetic field tensor F, split into ‘electric’ and ‘magnetic’ parts differently by each observer; the split is frame-dependent, the field is one object. A fail-loud self-check throws unless a rest-frame B of zero becomes nonzero under a boost. ◆ real electrodynamics/relativity, node-verified.
The leading field-transformation (perpendicular components, moderate γ) is shown; the full antisymmetric tensor also mixes parallel components and E²−c²B² stays invariant — the ‘a magnetic field appears under a boost’ result is exact.