numvana

Lorentz Force Calculator (Magnetic Force on a Moving Charge)

Find the magnetic force on a charged particle moving through a magnetic field, F = qvB sin(θ), from its charge, speed, field strength, and angle.

Magnetic force
0.5 N

How it works

A charged particle moving through a magnetic field feels a force F = |q| × v × B × sin(θ), where q is the particle's charge, v is its speed, B is the field strength, and θ is the angle between its velocity and the field direction — this is the magnetic part of the full Lorentz force law, F = q(E + v × B), with no electric field included here.

The sin(θ) factor means the force is strongest (F = |q|vB) when the particle moves perpendicular to the field, and zero when it moves exactly parallel or antiparallel to it — a charge coasting straight along field lines feels no magnetic force at all.

This gives the force's magnitude only. Its direction is always perpendicular to both the velocity and the field, following the right-hand rule for q(v × B) for a positive charge (reversed for a negative one), which is why it's a vector cross product rather than a plain multiplication.

FAQ

Why is the force zero when the angle is 0° or 180°?

sin(0°) and sin(180°) are both 0. Physically, the magnetic force comes from the v × B cross product, which vanishes whenever velocity and field point along the same (or exactly opposite) line — there's no component of motion for the field to deflect.

Why does the calculator ask for charge magnitude instead of a signed charge?

The formula here gives the force's magnitude, which only depends on how large the charge is, not its sign. A negative charge feels a force of the same size but in the opposite direction (via the right-hand rule reversed) — direction isn't something a single force-magnitude number can show.

Related calculators