Lorentz Force Calculator
When an electric charge moves through a magnetic field it feels a push, the magnetic part of the Lorentz force, and this calculator works out how strong that push is. Enter the charge, its speed, the magnetic field strength, and the angle between the direction of motion and the field, and it returns the force in newtons, updating as you type. The relationship is compact and revealing: the force is the charge times the speed times the field times the sine of the angle between the velocity and the field. Three features make it distinctive. First, the charge must be moving; a stationary charge feels no magnetic force at all. Second, the angle is crucial, because only motion across the field produces force, so the push is strongest when the charge moves at right angles to the field, where the sine is one, and vanishes when it moves straight along the field. Third, and most remarkably, the force always acts at right angles to both the velocity and the field, which means it constantly turns the charge without ever speeding it up, doing no work and instead bending the path into a circle or a spiral. That single fact explains an astonishing range of phenomena: the curved tracks of particles in detectors, the spiral of charged particles trapped in the Earth's magnetic field that creates the auroras, the operation of mass spectrometers and cyclotrons, and the force on the current-carrying wires inside every electric motor. That makes the tool genuinely useful for physics students learning about magnetic fields, charged particle motion and the motor effect and checking homework, and for anyone exploring electromagnetism. Use coulombs, metres per second and teslas for a force in newtons. The formula and a worked example are explained clearly below.
Scientific notation is accepted (e.g. 1.6e-19). The force is perpendicular to both v and B.
How it works
The magnitude of the magnetic force is F = q times v times B times the sine of the angle between the velocity and the field. It is maximum when the charge moves at right angles to the field (sine 90 is 1) and zero when it moves along the field (sine 0 is 0). The direction is at right angles to both, given by the right-hand rule.
Worked example
For a charge of 1.6 times 10 to the minus 19 coulombs moving at 1 million metres per second across a 0.5 tesla field at 90 degrees: the force is 1.6e-19 times 1e6 times 0.5 times 1, which is 8 times 10 to the minus 14 newtons.