Definition

Magnetic force

(E7.1.1) E7.1 · Force on a Moving Charge →

F = q v \times B

Statement

The force on a charge q moving with velocity v through a magnetic field B, perpendicular to both.

Symbols and units

$F$	magnetic force	N
$q$	charge	C
$v$	velocity	m/s
$B$	magnetic field	T

When it applies

Any moving charge in a magnetic field; defines B itself via the force observed.

Derivation

Defined directly by the observed force on a moving test charge — this relation is how the magnetic field itself is defined and measured.

F = q v \times B

Watch out for

Force is always perpendicular to velocity, so a magnetic field alone never does work on a charge or changes its speed — only its direction. A charge moving parallel to B feels no force at all.