Force on a Current Wire
Force on a current-carrying conductor.
Formula
Variables
How it works
A wire carrying an electric current in a magnetic field experiences a sideways force because the moving charges in the wire are pushed by the magnetic field. The force is strongest when the wire is perpendicular to the field and zero when it is parallel, which is why the sine of the angle appears. The formula combines the field strength, the current, the length of wire in the field, and the wire’s orientation to tell you how large that push is.
When to use it
Use this formula for problems involving a straight current-carrying conductor placed in a uniform magnetic field, such as electric motors, rail-gun style setups, or lab questions about magnetic force on wires. It is especially useful when you know the field strength, current, wire length inside the field, and the angle between the wire and the field.
Worked example, step by step
A 0.40 m wire carries a current of 3.0 A in a magnetic field of 0.80 T. The wire makes an angle of 60° with the field. Use F = BIL sinθ. F = (0.80)(3.0)(0.40)sin(60°) F = 0.96 × 0.866 F = 0.83136 N Final answer: F ≈ 0.83 N
Common mistakes to avoid
- using cosθ instead of sinθ
- forgetting that L must be the length of wire actually inside the magnetic field
- leaving out the angle factor and assuming the force is always BIL
Did You Know?
The sideways force on a current-carrying wire in a field is exactly what spins every electric motor.
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