Magnetic Force on a Current-Carrying Wire Calculator
Find the magnetic force on a straight current-carrying wire in a uniform magnetic field from the field strength, current, wire length and angle.
How it works
F = B·I·L·sin θ · Maximum when θ = 90° (wire perpendicular to the field)
A wire carrying current I in a magnetic field B experiences a force F = B·I·L·sin θ, where L is the length of wire in the field and θ is the angle between the wire and the field lines. The force is greatest when the wire is perpendicular to the field (sin 90° = 1) and vanishes when the wire runs parallel to it (sin 0° = 0). Its direction is given by the right-hand (or left-hand, for conventional-vs-electron flow) rule, always at right angles to both the current and the field. This is the force that turns every electric motor.
Worked example
A 0.2 m length of wire carrying 10 A sits perpendicular (90°) to a 0.5 T field: F = 0.5 × 10 × 0.2 × sin90° = 0.5 × 10 × 0.2 × 1 = 1 N. Tilting the wire to 30° to the field cuts the force to 0.5 × 10 × 0.2 × 0.5 = 0.5 N.
Frequently asked questions
When is the magnetic force on a wire greatest?
When the wire is perpendicular to the field, because sin θ reaches its maximum of 1 at θ = 90°. When the wire lies along the field lines (θ = 0°), sin θ is zero and there is no force at all.
Which way does the force point?
It is perpendicular to both the current and the magnetic field, in the direction given by the right-hand rule (point fingers along the current, curl toward the field; the thumb-type result gives the force). Electric motors use exactly this to convert current into rotation.
What is a tesla?
The tesla (T) is the SI unit of magnetic flux density: one tesla produces one newton of force per metre on a wire carrying one ampere perpendicular to it. It is a strong unit — the Earth’s field is about 0.00005 T, while an MRI magnet is 1.5–3 T.
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This calculator is for educational purposes. Double-check important results before acting on them.