Lorentz Force Law

$$F = q(\mathbf{v} \times \mathbf{B})$$

Status: Proven.

The force on a charged particle $q$ moving with velocity $\mathbf{v}$ through a magnetic field $\mathbf{B}$. One of the foundational equations of classical electromagnetism, combined with the electric-field force term ($qE$) into what’s generally called “the Lorentz force.”

Real, independent confirmation: this equation is the working basis of every technology that steers or accelerates charged particles with magnetic fields — mass spectrometers, particle accelerators, cathode-ray tubes, electric motors. Confirmed continuously, not a contested result.

Used in: Paper 3, reused unmodified in a worked numerical example (this session’s own audit found the specific example’s arithmetic off by about 6x — within normal rounding for an illustrative calculation, not flagged as a significant error). PBT proposes a mechanical account of magnetic fields, not a change to this force law itself.