This magnetic force calculator covers both Lorentz-force forms: on a moving charge (F = qvB·sinθ) and on a current-carrying wire (F = BIL·sinθ) — the physics inside motors, mass spectrometers and railguns.
The Sideways Force: No Push Along the Motion, Ever
Part of our Physics Calculators collection.
Worked Examples (Verified)
- Proton at 10⁶ m/s in 0.5 T (defaults): F = 1.602 × 10⁻¹⁹ × 10⁶ × 0.5 = 8.01 × 10⁻¹⁴ N — tiny in newtons, enormous for a proton: it curves the beam in a radius of about 2 cm (r = mv/qB)
- Wire: 10 A, 2 m in 0.5 T (wire mode): F = 0.5 × 10 × 2 = 10 N — kilogram-scale force from a benchtop setup; scale the current and you have motors, loudspeakers and maglev
- θ is the silent factor: at θ = 0° (motion parallel to B) the force is exactly zero — field-aligned charges travel untouched, the reason helical paths have a constant forward drift
Force Discipline
- Right-hand rule for direction: fingers along v (or I), curl toward B, thumb gives F for positive charge; negative charges flip it.
- Magnetic forces never change speed or kinetic energy (F ⊥ v always) — accelerators use ELECTRIC fields for energy and magnets purely for steering.
- 1 T is a strong lab field (MRI: 1.5–3 T); Earth’s field is ~50 µT — the B in most textbook problems is wildly un-Earthlike, by design.
- The wire formula is the charge formula in bulk: BIL is just (total moving charge) × (drift velocity) summed along the wire.
Related Tools
- Electric Field Calculator — the E half of electromagnetism
- Coulomb’s Law Calculator — charge forces
- Physics Calculators — the full collection
Frequently Asked Questions
How do you calculate magnetic force on a charge?
F = |q|·v·B·sinθ — charge × speed × field × sine of the angle between velocity and field. A proton (1.602 × 10⁻¹⁹ C) at 10⁶ m/s perpendicular in 0.5 T feels 8.01 × 10⁻¹⁴ N. This calculator covers both this Lorentz force and the wire form.
How do you calculate force on a wire in a magnetic field?
F = B·I·L·sinθ — field × current × length of wire inside the field × sine of the angle between current and field. 0.5 T × 10 A × 2 m at 90° = 10 N. It’s the summed Lorentz force on the wire’s drifting charges, and the operating principle of electric motors.
Why doesn’t a magnetic field speed particles up?
The force is always perpendicular to velocity (it’s a cross product, v × B), so it can only rotate the velocity vector, never stretch it. Work = F·displacement along motion = 0 at every instant. Charged particles circle or helix at constant speed.
What happens at θ = 0° or 180°?
sin θ = 0 → zero force. Motion exactly along (or against) the field lines is undeflected; combined with any perpendicular component, particles trace helices around the field lines — how auroras funnel toward the poles.
What radius does a charged particle circle at?
r = mv/(|q|B) — the magnetic rigidity relation behind mass spectrometers and cyclotrons. For the default proton: (1.673 × 10⁻²⁷ × 10⁶)/(1.602 × 10⁻¹⁹ × 0.5) ≈ 0.021 m ≈ 2 cm. Heavier or faster particles swing wider; stronger fields tighten the circle.
Is this magnetic force calculator free?
Yes — free, instant, no sign-up.