Magnetic Force Calculator

About the Magnetic Force Calculator

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.

When This Page Helps

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.

How to Use the Inputs

1. Select the force scenario: charged particle, current-carrying wire, or parallel wires.
2. For charged particles: enter charge, velocity, magnetic field strength, and angle.
3. For current-carrying wires: enter current, wire length, field strength, and angle.
4. For parallel wires: enter both currents and the separation distance.
5. View force magnitude, direction, and related calculations.
6. Use presets for common physics scenarios.
7. Compare results in the reference table.

Example Calculation

Tips & Best Practices

• The magnetic force on a charged particle is always perpendicular to its velocity — it acts as a centripetal force.
• For maximum force, the angle between v (or I) and B should be 90°. At 0° or 180°, the force is zero.
• The cyclotron radius increases with particle momentum but the period stays constant — key for accelerator design.
• In a uniform magnetic field, charged particles follow helical paths if they have a velocity component along B.
• For practical motor calculations, remember F = BIL gives force per conductor. Multiply by number of conductors.
• The force between household wires (~15A, ~cm apart) is very small — milliNewtons per meter.

The Lorentz Force and Particle Motion

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.

Force on Current-Carrying Conductors

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.

Engineering Applications

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.

Frequently Asked Questions

• What is the Lorentz force?

  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.

• Why does a magnetic force do 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.

• What determines force direction?

  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.

• How do electric motors use magnetic force?

  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.

• What is cyclotron frequency?

  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.

• Do parallel wires attract or repel?

  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.