Electromagnetic Force (Lorentz) Calculator

The Lorentz force is calculated using F = q(E + v×B), where q is the charge, E is the electric field strength, v is the velocity, and B is the magnetic field strength. The magnetic component also depends on the angle between velocity and magnetic field vectors. See also our Faraday's Law Calculator.

For an electron (charge = -1.6×10⁻¹⁹ C) moving perpendicular to a 0.5 T magnetic field, the force depends on its velocity. At 10⁶ m/s, the magnetic force would be approximately 8×10⁻¹⁴ N perpendicular to both velocity and field directions.

The magnetic component of Lorentz force is always perpendicular to both the velocity vector and magnetic field vector. Use the right-hand rule for positive charges: point fingers in velocity direction, curl toward magnetic field, thumb points in force direction. For negative charges, the force is opposite.

You need five key parameters: particle charge (q), particle velocity (v), electric field strength (E), magnetic field strength (B), and the angle between velocity and magnetic field vectors. The calculator can solve for any missing parameter if the others are provided. You might also find our Electromagnetic Wave Calculator useful.

Lorentz force is fundamental in many devices including electric motors, particle accelerators, mass spectrometers, cathode ray tubes, and magnetic levitation systems. It's also crucial in understanding plasma physics and the behavior of charged particles in space.

The magnetic component of Lorentz force depends on sin(α), where α is the angle between velocity and magnetic field. Maximum force occurs at 90° (perpendicular), while no magnetic force acts when the particle moves parallel to the field (0° or 180°).

Lorentz force calculators are highly accurate for classical physics applications. They use the fundamental electromagnetic equations and provide precise results within the limits of classical mechanics. For relativistic speeds (near light speed), relativistic corrections may be needed.