Magnetic Force on Charge Calculator
A charged particle moving through a magnetic field experiences the Lorentz magnetic force F = q * v * B * sin(theta), where q is charge in coulombs, v is speed in m/s, B is magnetic flux density in teslas, and theta is the angle between the velocity and the magnetic field direction. The force is always perpendicular to both the velocity and the magnetic field, causing the particle to curve but not change speed. This principle underlies electric motors, cathode ray tubes, mass spectrometers, and particle accelerators.
Magnetic force formula
F = q * v * B * sin(theta)
q is charge in coulombs, v is speed in m/s, B is magnetic field in teslas, theta is the angle between v and B in degrees. Example: q = 1 uC = 1e-6 C, v = 500 m/s, B = 0.5 T, theta = 90 degrees: F = 1e-6 * 500 * 0.5 * sin(90) = 1e-6 * 500 * 0.5 * 1 = 0.00025 N.
Magnetic force applications
- Electric motors: current-carrying conductors in a magnetic field experience a force (F = BIL sin theta) that drives shaft rotation.
- Mass spectrometers: ions of different masses follow circular paths of different radii in a magnetic field, allowing mass separation.
- Cyclotrons: protons are accelerated in a spiral path by combining a magnetic field (to curve) and an electric field (to accelerate).
- Hall effect sensors: moving charge carriers in a conductor are deflected by a magnetic field, producing a measurable transverse voltage proportional to B.
Frequently asked questions
What is the Lorentz magnetic force formula?
The magnetic force on a moving charge is F = q * v * B * sin(theta), where q is charge in coulombs, v is speed in m/s, B is magnetic field strength in teslas, and theta is the angle between the velocity vector and the magnetic field vector.
When is the magnetic force maximum?
The force is maximum when the charge moves perpendicular to the magnetic field (theta = 90 degrees), giving F = q * v * B. The force is zero when the charge moves parallel or anti-parallel to the field (theta = 0 or 180 degrees).
What direction does the magnetic force act?
The magnetic force direction is given by the right-hand rule for positive charges: point fingers in the direction of v, curl them toward B, and the thumb points in the direction of F. For negative charges, the force is in the opposite direction.
Does the magnetic force do work on the charge?
No. The magnetic force is always perpendicular to the velocity of the charge, so it does no work and cannot change the particle's kinetic energy. It can only change the direction of motion, causing circular or helical paths in uniform fields.
What is the radius of circular motion of a charge in a magnetic field?
When theta = 90 degrees, the magnetic force provides centripetal acceleration. The radius of the circular path is r = m * v / (q * B), where m is the particle mass. This is the basis for cyclotrons and mass spectrometers.
Official sources
- NIST: NIST SP 811, Guide for SI Units.
- OpenStax University Physics: Magnetic Force, Vol. 2 Ch. 11.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.