How this calculator works
The magnetic force is the cross product of charge times velocity with magnetic flux density. Its magnitude uses the absolute charge and the sine of the angle. The right-hand rule gives the force direction for positive charge; reverse it for negative charge. Magnetic force is perpendicular to motion and does no work on a point particle. The full Lorentz law also includes qE, which is outside this magnetic-only calculation.
Formula
Fmag = |q| v B sin(theta), with 0 <= theta <= pi. theta = asin(Fmag/(|q|vB)); pi - theta is also possible. Full vector law: F = q(E + v cross B).
Worked example
A charge magnitude 2 C moving at 3 m/s through 4 T at 90 degrees feels 24 N. At zero angle, the force is zero even for a nonzero negative charge.
Advertisement
Frequently asked questions
Why does a negative charge give positive force here?
The result is a magnitude. A negative charge reverses direction, not magnitude.
Why are two angles returned?
Sine is the same for supplementary angles. A force magnitude alone cannot distinguish them.
Does a magnetic field increase particle speed?
The ideal magnetic force changes direction rather than kinetic energy because it is perpendicular to velocity.