How this calculator works
The magnetic Lorentz forces on moving charge carriers combine into a force on a current-carrying conductor. Only the component of the wire perpendicular to the field contributes. The straight-wire formula assumes a uniform field and steady current. Inverting the sine gives two supplementary angles in the allowed zero-to-pi range; both are displayed.
Formula
F = B I l sin(theta); theta = asin[F/(B I l)], with supplementary solution pi-theta.
Worked example
A 4 m wire carrying 3 A perpendicular to a 2 T field experiences 24 N. A 12 N force on 3 m in the same field implies 2 A when the wire is perpendicular.
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Frequently asked questions
What happens when the wire is parallel to the field?
The magnetic force is zero. Zero force then does not uniquely determine B, I or length.
How do I determine force direction?
Use the vector cross product I l × B, taking l in the direction of conventional current.
Can I use this for a curved wire?
For a curved wire or varying field, integrate I dl × B over the path. A single angle and length may not represent the geometry.