/field studies  ·  [ fig. 04 ]  lorentz force

A field that pushes
only sideways

F = qv × B is always perpendicular to the motion, so it can turn a particle but never speed it up. Drag the velocity arrow: whatever points along B carries straight on, whatever points across it curls into a circle. Together they make a helix.

whatA charged particle launched into a uniform magnetic field, its path integrated step by step from the equation of motion. lawF = qv × B. The force is perpendicular to the velocity, so it changes direction but never speed — kinetic energy is untouched. trySet the axial velocity to zero, then raise |B|. noticeThe helix collapses into a flat circle whose radius falls as 1/B. Restore the axial component and that circle stretches into a helix of the same radius. in lifeMass spectrometers and cyclotrons use the gyroradius to sort particles; the aurora is the same helix around Earth's field. found byNamed for Hendrik Lorentz, who wrote the full force law in 1895, building on Maxwell and Heaviside.
Orbit geometry
gyroradius r = mv⊥ / |q|B
THE PARTICLE — DRAG TO REPOSITION
VELOCITY TIP — DRAG TO AIM
B FIELD — UNIFORM, ALONG Z
DRAG EMPTY SPACE — ORBIT
DRAG PARTICLE OR ARROW TIP
SCROLL — ZOOM