Lorentz Force

The Lorentz Force

A charged particle moving through a magnetic field experiences a force perpendicular to both its velocity and the field:

$F = qvB quad ( ext{when } v perp B)$

• F — magnetic force (N)
• q — charge (C)
• v — speed (m/s)
• B — magnetic field strength (T)

Direction

The force direction follows the right-hand rule (or left-hand for negative charges): fingers point along v, curl toward B, thumb points along F.

Full Vector Form

ec{F} = q(ec{v} imes ec{B})

The cross product means the force is always perpendicular to velocity — a magnetic field does no work on a charge. Instead it deflects moving charges into circular orbits, which is how cyclotrons and mass spectrometers work.

Circular Motion in a Field

For circular orbit of radius r:

r = rac{mv}{qB}

Examples (v ⊥ B)

Your Task

Implement lorentz_force(q, v, B) returning the force magnitude (assuming $v perp B$).