Force on a Current-Carrying Wire

F = B · I · L · sin(θ)

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Result
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Formula

F = B × I × L × sin(θ)

Description

A wire carrying current in a magnetic field experiences a force equal to the field times the current times the length of conductor in the field, scaled by the sine of the angle between current and field. This is the motor principle: it converts electrical current into mechanical force. The direction is given by the right-hand (or Fleming’s left-hand) rule.

Variables

  • F — Force on the conductor (N)
  • B — Magnetic flux density (T)
  • I — Current (A)
  • L — Length of conductor in the field (m)
  • θ — Angle between current and field (degrees)

Practical Notes

Force is maximum when the wire is perpendicular to the field (θ = 90°). This force times radius gives motor torque; it is also the loudspeaker drive force on the voice coil.

Related Concepts

All Fields & Electromagnetism formulas →
Coulomb’s Law Electric Field of a Point Charge Electric Potential of a Point Charge Gauss’s Law (Electric Flux) Lorentz Magnetic Force Force on a Current-Carrying Wire Force Between Parallel Wires Magnetic Field of a Straight Wire

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