Physics 12.13 - Force on a current-carrying conductor

Force, field, current and length

Fleming’s left-hand rule predicts force direction. To calculate the magnitude for a straight conductor at right angles to a uniform magnetic field, use:

The symbol $l$ is a lower-case L, not the number 1. A wire may be long, but only its section within the magnetic field contributes to this calculation. The equation above applies when the wire and field are perpendicular; do not use it as the full force for any angle.

For fixed field and length, doubling current doubles force. Similarly, doubling either $B$ or $l$ alone doubles force. Reversing current changes force direction, but keeping its magnitude unchanged keeps the same force magnitude.

Converting units and calculating force

Worked example: finding force

A $6.0\,\mathrm{cm}$ wire section is perpendicular to a field of flux density $0.45\,\mathrm{T}$. It carries $2.8\,\mathrm{A}$. Calculate the force.

Convert the length before substituting:

To two significant figures, the force is $0.076\,\mathrm{N}$. Using 6.0 as the length in metres would give a force 100 times too large. A small force is reasonable for this short wire.