Magnetic Force Calculator (Lorentz Force)
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
The magnetic component of the Lorentz force is calculated with F = q × v × B, for a velocity perpendicular to the magnetic field. A 1-microcoulomb charge at 1000 m/s in a 0.5-tesla field experiences a force of about 0.0005 N.
Explanation
A stationary electric charge in a magnetic field experiences no magnetic force at all: it's only its motion that triggers this interaction, a fundamental difference from the electric force described by Coulomb's law, which acts between charges even at rest. The magnetic force, in the simplest case where the charge's velocity is perpendicular to the magnetic field, is directly proportional to the three quantities involved: the charge itself, its velocity, and the magnetic field's strength. A remarkable feature of this force is that it's always perpendicular to both the charge's velocity and the magnetic field — it therefore never changes the speed (the magnitude of the velocity) of a moving charge, only its direction, which produces the characteristic circular or helical trajectories. This principle is directly exploited in many technologies: particle accelerators use powerful magnetic fields to curve the path of charged particles at very high speed without slowing them down, mass spectrometers separate ions by their differently curved trajectories depending on their charge-to-mass ratio, and electric motors exploit this force on moving charges in a conductor to produce mechanical motion. This same magnetic field is also what a current-carrying wire creates around itself, as covered by our straight wire magnetic field calculator — the moving charges inside that wire experience exactly this same Lorentz force from each other's collective field.
Example: a 1 µC charge at 1000 m/s in a 0.5 T field
Inputs
Charge: 1×10⁻⁶ C. Velocity: 1000 m/s. Magnetic field: 0.5 T.
Calculation
F = 1×10⁻⁶ × 1000 × 0.5 = 0.0005 N.
Result
This charge experiences a magnetic force of about 0.0005 N (0.5 mN).
Frequently asked questions
Why does the magnetic force never change a charge's speed, only its direction?
Because the magnetic force is always oriented perpendicular to the charge's direction of motion, a direct consequence of its full vector formula (a cross product between velocity and magnetic field). A force perpendicular to motion can do no work on the charge (in the physical sense of the term), so it can neither speed it up nor slow it down: it only continuously curves its path, never changing the speed of travel itself.
What happens if the velocity isn't perpendicular to the magnetic field?
The full formula becomes F = q×v×B×sin(θ), where θ is the angle between the velocity and the magnetic field: the force decreases as this angle moves away from 90°, becoming zero when the velocity is perfectly parallel to the field (sin(0°)=0), a case where the charge's motion crosses no magnetic field lines at all. This calculator is deliberately limited to the perpendicular case, the most common in everyday and educational use.
How is this force used in a mass spectrometer?
A mass spectrometer sends charged ions through a magnetic field, where the magnetic force curves their path along a radius that depends directly on their mass-to-charge ratio. Heavier ions (at equal charge) are deflected less and follow a larger-radius path, which allows them to be separated and identified by mass, an essential technique in analytical chemistry.