Lorentz Force⚠ unverified
Physics / Electromagnetics · Compute the magnitude of the Lorentz force on a moving charge
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| q | q | C | 1.0 | Charge of the particle |
| E | E | V/m | 1.0 | Electric field magnitude |
| v | v | m/s | 1.0 | Speed of the particle |
| B | B | T | 1.0 | Magnetic flux density |
| theta | θ | — | 90.0 | Angle between the velocity and the magnetic field, in degrees. Default is 90.0 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | F | N | Magnitude of the Lorentz force, in newtons (N) |
The science & history
Understanding the Parameters
- $q$, $E$ — electric part $qE$.
- $v$, $B$, $\theta$ — magnetic part magnitude $q v B\sin\theta$ (zero when $\mathbf{v}\parallel\mathbf{B}$).
- Combined — Pythagorean sum assumes the electric and magnetic force vectors are perpendicular.
Derivation (Approaching a Proof)
Magnetic force $q\mathbf{v}\times\mathbf{B}$ is always perpendicular to $\mathbf{v}$ (no magnetic work). Electric force $q\mathbf{E}$ is independent of velocity. The registry formula is the Euclidean norm of two orthogonal contributions $qE$ and $q v B\sin\theta$, not the general vector sum for arbitrary orientations of $\mathbf{E}$.
History
H. A. Lorentz formulated the force on charges in EM fields; it is fundamental to cyclotron motion, Hall effect, and plasma dynamics.
Related Concepts: Magnetic Force, Coulomb's Law force, Magnetic Field Wire, Induced Emf
Notes: Registry calculator lorentz-force (unverified). Special-case magnitude (E ⊥ magnetic
force). Confirm whether $\theta$ is degrees or radians in the live solver.