Calculate magnetic force on charged particles, current-carrying wires, and between magnets. Supports Lorentz force, force between wires, and dipole interactions.
The Magnetic Force Calculator computes forces in electromagnetic systems using three fundamental scenarios: the Lorentz force on a charged particle moving through a magnetic field (F = qv × B), the force on a current-carrying wire in a magnetic field (F = BIL sin θ), and the force between two parallel current-carrying wires (F/L = μ₀I₁I₂ / 2πd). It gives a quick way to connect field strength, current, motion, and mechanical force in one place.
These calculations are foundational in physics and engineering — from particle accelerator design to electric motor engineering to power transmission line mechanics. The Lorentz force is responsible for the circular motion of charged particles in magnetic fields, the basis of cyclotrons and mass spectrometers.
Enter values for any scenario and get force magnitudes, directions, and related quantities like cyclotron radius, particle kinetic energy, and work done. The calculator includes presets for common engineering and physics scenarios. It gives you a single place to compare charge, current, and field interactions without re-deriving each formula.
Use this calculator when you need a fast magnetic-force result for a particle, a wire, or a parallel-conductor setup without switching between separate formulas. It is useful for motor intuition, field-force checks, and physics problems that combine current, motion, and magnetic flux density in the same calculation. That makes it easier to see whether the force magnitude is actually plausible.
Lorentz Force: F = qvB sin θ. Wire in Field: F = BIL sin θ. Parallel Wires: F/L = μ₀I₁I₂ / (2πd). Cyclotron Radius: r = mv / (qB). Period: T = 2πm / (qB).
Result: F = 8.0 × 10⁻¹⁴ N
An electron (q = 1.6×10⁻¹⁹ C) moving at 10⁶ m/s perpendicular to a 0.5 T field: F = 1.6×10⁻¹⁹ × 10⁶ × 0.5 × sin(90°) = 8.0×10⁻¹⁴ N. The electron follows a circular path with radius r = mv/(qB) = 0.0114 mm.
When a charged particle enters a uniform magnetic field perpendicular to its velocity, it follows a circular path. The magnetic force provides the centripetal force: qvB = mv²/r, giving the cyclotron radius r = mv/(qB). Particles with higher momentum trace larger circles, which is the basis of mass spectrometry.
If the particle has a velocity component parallel to B, the motion becomes helical — circular in the plane perpendicular to B, with uniform motion along B. This is how charged particles spiral along Earth's magnetic field lines, creating auroras.
The force F = BIL sin θ on a current-carrying wire is the macroscopic manifestation of the Lorentz force on many moving charges. In a motor, this force creates torque. In a railgun, it accelerates a projectile. In an MHD generator, it converts kinetic energy of conducting fluid to electricity.
The direction follows the right-hand rule with current replacing velocity. This force is the operating principle of every DC motor, every loudspeaker, and every electromagnetic relay.
Understanding magnetic forces is crucial in designing electromagnetic actuators, transformers, generators, and particle beam systems. Engineers must account for forces on busbars in power plants (hundreds of kA during faults), forces between superconducting coils in fusion reactors (millions of Newtons), and the tiny forces on MEMS devices in sensors.
The Lorentz force is the force on a charged particle moving through electric and magnetic fields: F = q(E + v × B). The magnetic component F = qv × B is always perpendicular to the velocity, so it changes direction but not speed — it does no work.
The magnetic force is always perpendicular to the velocity of the charged particle (F = qv × B). Since work = F · displacement and displacement is along v, the dot product F · v = 0. The force changes direction but not kinetic energy.
The right-hand rule: point fingers in the direction of v (or current), curl them toward B, and the thumb points in the force direction for positive charges. For negative charges (electrons), the force is in the opposite direction.
Motors use F = BIL to convert electrical energy to mechanical energy. Current flows through coils in a magnetic field, creating forces that produce torque. By switching current direction as the rotor turns (commutation), continuous rotation is achieved.
The cyclotron frequency f = qB/(2πm) is the frequency at which a charged particle orbits in a uniform magnetic field. Remarkably, this frequency is independent of the particle's speed — faster particles have larger orbits but complete them in the same time.
Parallel wires with currents in the same direction attract. Opposite currents repel. This is actually how the Ampere was originally defined: the current that produces 2×10⁻⁷ N/m force between two wires 1 m apart.