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Force on a current-carrying wire
Intermediate
Force on a wire in a magnetic field.
F = BIL sinθF = I L × B, magnitude BIL sinθ. It is the sum of forces on moving charges. The right-hand rule gives direction.
A 0.5 m wire carrying 10 A in 0.2 T: 1 N.
Zero when the wire is parallel to B.
In more detail
A current-carrying wire in a magnetic field experiences a force F = BIL sin θ, perpendicular to both the wire and the field. The force comes from the magnetic force on moving charges in the wire.
Real-world uses
- Electric motors rely on forces on current-carrying coils.
- Railguns use the force on current-carrying rails.
- Electric motors depend on the force on a current-carrying wire in a magnetic field to produce turning motion.
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Frequently asked questions
Which direction does the force act?
Use Fleming's left-hand rule: thumb for force, first finger for field, second finger for current.
Why is there no force on a wire parallel to the field?
Because sin θ is zero, so the force is zero.
Why is the force largest when the wire is perpendicular to the field?
The sine factor is largest at 90 degrees, so the force is greatest when the current is at right angles to the field.
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