Magnetic Force on a Current-Carrying Wire Calculator NZ
This calculator finds the magnetic force on a current-carrying wire placed in a magnetic field, the effect that makes electric motors turn. When a wire carrying an electric current sits in a magnetic field, the field exerts a force on the moving charges in the wire, and so on the wire itself. This force is the principle behind every electric motor, loudspeaker and many other devices: a current in a field produces motion. The size of the force depends on the strength of the magnetic field, the current flowing, the length of wire in the field, and the angle between the wire and the field, being greatest when they are at right angles and zero when the wire lies along the field. This calculator computes it. You enter the magnetic field strength in tesla, the current in amps, the length of wire in the field in metres, and the angle between the wire and the field in degrees, and the calculator returns the force in newtons, the perpendicular factor from the angle, and the force per metre of wire. The results update as you type. Use it for physics study, for understanding motors and electromagnetic devices, or for any problem involving a conductor in a magnetic field. The force is the field strength times the current times the length times the sine of the angle. The sine term means orientation matters: at ninety degrees the force is at its maximum, while a wire lying parallel to the field feels no force at all, since the sine of zero is zero. The direction of the force is given by the motor rule, perpendicular to both the current and the field. This relationship, force equals field times current times length, is one of the cornerstones of electromagnetism, connecting electricity and magnetism to mechanical motion, and it is exactly what an electric motor exploits to produce rotation.
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1 N
magnetic force
Perpendicular factor1
Force per metre5 N/m
Field0.5 T
Force = field x current x length x sine of the angle. Maximum at 90 degrees; zero when the wire lies along the field. The basis of electric motors. Rounded for display.
How it works
The magnetic force on a current-carrying wire is the magnetic field strength multiplied by the current, the length of wire in the field, and the sine of the angle between the wire and the field. At ninety degrees the sine is one, giving the maximum force, while at zero degrees the sine is zero and there is no force.
Worked example
A 0.2 metre wire carrying 10 amps in a 0.5 tesla field at right angles experiences a force of 0.5 times 10 times 0.2 times the sine of 90 degrees, which is 0.5 times 10 times 0.2 times 1, equalling 1 newton. The force per metre of wire is 5 newtons per metre.
