Tools / Physics
100% client-side · 5-way solver · right-hand-rule diagramThe Ampère force on a straight wire in a uniform magnetic field. Solve for any of the five quantities — force, current, length, field or angle — then switch to square-loop mode for the force on each side of a current loop plus its torque.
| Fmax = I·L·B (θ = 90°) | — |
|---|---|
| sinθ factor | — |
| Direction (right-hand rule) | — |
| Supplementary angle | — |
Equivalent: Fleming's left-hand rule — forefinger along B, middle finger along I, thumb gives F. Same answer; it is the classic "motor rule".
Loop of side L, current I, uniform field B in the plane of the loop at angle α to the axis of side-pair A (sides 1 & 3). Each side feels F = I·L·B·sin(angle between its current and B); opposite sides cancel, so the net force is always zero — but the loop feels a torque τ = I·A·B.
| Force on sides 1 & 3 (pair A) | — |
|---|---|
| Force on sides 2 & 4 (pair B) | — |
| Net force on the loop | — |
| Torque axis | — |
⊙ = force out of the screen, ⊗ = into the screen. Current runs clockwise (red arrows); sides 1–4 are numbered inside the loop.
F = I·L·B·sinθ, also called the Ampère force. I is the current in amperes, L the wire length in metres inside the field, B the magnetic flux density in tesla, and θ the angle between the current direction and B. In vector form F = I·(L × B): the force is perpendicular to both the wire and the field, and its size is in newtons.
F = 5 × 0.2 × 0.5 × sin 90° = 1.0 × 0.5 × 1 = 0.5 N. That is the anchor this calculator reproduces exactly — the defaults on the straight-wire tab are these very numbers, so press Calculate to verify.
Because of the sinθ factor: at θ = 0° (or 180°) sinθ = 0, so a wire lying along the field lines feels nothing. Only the component of B perpendicular to the wire does work on the charges, which is why the force is maximal (F = I·L·B) at θ = 90°.
Point the fingers of your right hand along the current I, curl them toward the magnetic field B through the smaller angle, and your thumb points along F. For 0° < θ < 180° the force in this calculator's diagram comes out of the screen. Fleming's left-hand rule (forefinger B, middle finger I, thumb F) is the equivalent motor rule and gives the same answer.
F = q·v×B acts on one moving point charge (cyclotron, mass spectrometer, aurora physics) — that is our Lorentz Force Calculator. F = I·L×B acts on a current in a wire (motors, rails, galvanometers). They are the same physics summed up: a wire of cross-section A carries n·q·vd·A of drift charge per second, and adding q·vd×B over the n·A·L carriers in length L gives exactly I·L×B.
In a uniform field, opposite sides of the loop carry antiparallel currents, so their forces are equal and opposite and cancel. With B in the loop's plane at angle α to side-pair A: sides 1 & 3 feel I·L·B·sinα each, sides 2 & 4 feel I·L·B·cosα each. Example: I = 2 A, L = 0.1 m, B = 0.5 T, α = 30° → 0.05 N per side on pair A, 0.0866 N per side on pair B, net force 0 N, torque τ = I·A·B = 0.01 N·m. That torque is what spins an electric motor.
Invert the formula: θ = arcsin(F / I·L·B). There are always two answers, θ and 180° − θ, because sinθ is symmetric — the calculator shows both. If F exceeds I·L·B the ratio is above 1 and no angle exists: such a force is physically impossible with those I, L and B, and the calculator rejects it instead of inventing a number.
1 tesla = 10,000 gauss (G). The calculator accepts T, mT, µT and G. A fridge magnet is about 5 mT = 50 G; Earth's field is roughly 25–65 µT — a 5 A, 0.1 m wire in a 50 µT field at 90° feels just 5 × 0.1 × 50×10⁻⁶ = 2.5×10⁻⁵ N = 25 µN.
Everywhere current meets magnetism: the torque on rotor loops in electric motors, the moving coil of galvanometers and loudspeakers, railgun armatures, and the forces that circuit breakers must survive during a fault. Our Electric Motor Torque calculator continues where the square-loop mode here leaves off.
Free tool by NRTechStudio
Explore similar science tools and calculators. 100% free, accurate, and runs completely in your browser without sign-up.
2 taps, no typing needed — diagnostics are sent automatically.