Magnetic Force Calculator

Magnetic force on a moving charge

A charge moving through a magnetic field feels a force perpendicular to both its velocity and the field. Its magnitude is

F = |q| × v × B × sin θ

where q is the charge (coulombs), v the speed (m/s), B the magnetic field (teslas) and θ the angle between the velocity and the field. The force is greatest when the velocity is perpendicular to the field and zero when it is parallel. A charge at rest feels no magnetic force. The direction follows the right-hand rule.

Circular path

If the charge enters at right angles to the field, the force stays perpendicular to the velocity and bends the path into a circle. The magnetic force supplies the centripetal force: |q| × v × B = m × v² / r. So

r = m × v / (|q| × B) and T = 2 × π × m / (|q| × B)

The period does not depend on the speed: a faster particle follows a bigger circle but takes the same time for each turn. The cyclotron relies on this.

Current-carrying wire

A current is charge in motion. The force on a straight wire of length L in a magnetic field is

F = B × I × L × sin θ

This is the force that turns electric motors.

Example

A proton entering a 0.5 T field at right angles with a speed of 1 000 000 m/s moves in a circle of radius 2.09 cm and completes each turn in 131 nanoseconds. A wire carrying 5 A at right angles to a 0.30 T field feels 0.30 × 5 × 1 = 1.5 N on each metre of its length.

Limits

The field is taken as uniform. The tool gives the magnitude of the force, and you find the direction with the right-hand rule. Close to the speed of light the radius is calculated with relativistic momentum.