Magnetic Force on a Wire Calculator

A conductor carrying electric current experiences a force when it lies in a magnetic field. At the microscopic level, moving charge carriers experience the Lorentz force. The forces transferred through the conductor combine into the macroscopic wire relation F = BIL sin(θ), where B is magnetic flux density, I is current, L is the wire length inside the field, and θ is the angle between conventional current direction and the magnetic field. The result is measured in newtons when SI units are used. Only the magnetic field component perpendicular to current contributes. This component is B sin(θ), which the calculator reports along with force. A wire perpendicular to the field at 90 degrees experiences maximum force. A wire parallel or antiparallel to the field at 0 or 180 degrees has zero magnetic force because the cross product vanishes. Angles with the same sine produce the same force magnitude, though vector direction still depends on the actual orientation. Use Fleming's left-hand rule or the vector product L × B to determine force direction. Point the current-length vector with conventional current and combine it with magnetic field direction; the force is perpendicular to both. Reversing either current or field reverses force. Reversing both leaves force direction unchanged. This calculator reports magnitude rather than a three-dimensional vector, so direction must be established from the physical arrangement. The equation assumes a straight segment, uniform field, steady current, and a wire thin enough that the same field applies across it. If field strength changes along the conductor, calculate the vector force by integrating I dL × B over the path. Curved wires can also require segment-by-segment vector addition. The active length is only the portion actually inside the magnetic field, not necessarily the conductor's total length. Enter amperes, metres, teslas, and degrees exactly as labelled. This relation supports motor-force estimates, electromagnetic actuator analysis, loudspeaker examples, laboratory demonstrations, and introductory physics problems. Real equipment may also need thermal, mechanical, fringe-field, and support-force analysis. The output provides a reliable ideal value and exposes the perpendicular field component so you can see directly how orientation reduces force from its maximum BIL value.