D.3.5—Force on current conductor

Use the conductor equation

Here $L$ is only the conductor length inside the uniform field and $\theta$ is the angle between conventional current and the field. Direction follows the force rule for conventional current.

Worked example — measuring a field

A perpendicular wire carries $I=1.64\,\mathrm{A}$ through $L=8.13\,\mathrm{cm}=0.0813\,\mathrm{m}$ and experiences $F=4.12\times10^{-4}\,\mathrm{N}$. Thus $B=F/(IL)=(4.12\times10^{-4})/(1.64\times0.0813)=3.09\times10^{-3}\,\mathrm{T}$.

Read the angle limits

The force is zero when the wire is parallel to the field and maximum when it is perpendicular. Use conventional current direction for the force rule, not the electron drift direction.

Connect the models

The conductor formula is the combined magnetic force on moving charge carriers: $I=q/t$ and $L=vt$ lead from $F=qvB\sin\theta$ to $F=BIL\sin\theta$.

Common trap

Do not use electron motion as the current direction, and do not include wire length outside the region where the magnetic field exists.