Magnetism
Force on a conductor
- where
- force on the conductor (N)
- flux density (T)
- current (A)
- conductor length (m)
- angle between current and field (°)
Explain this equation
Gives the force on a current-carrying conductor in a magnetic field. It is the principle behind every electric motor and the forces on busbars during a fault.
B is flux density in tesla. I is the current in amperes. l is the length of conductor inside the field, in metres. θ is the angle between the current direction and the field. sin θ keeps only the part of the conductor lying across the field. F is the force in newtons.
The moving charges in the conductor are pushed sideways by the field. More field, more current or more length gives proportionally more force. Current running along the field lines feels no push, so sin 0° gives zero.
0.5 T, 2 A and 3 m at right angles gives 3 N. At 30° the force halves to 1.5 N. Double the current and the force doubles.
Watch out: this gives the size of the force only; use the left-hand rule for its direction. Use sin, not cos, for this angle.
A current-carrying conductor in a magnetic field experiences a force. The effect is greatest at right angles to the field.
This relationship underpins motor force. Direction is separate from the magnitude calculation.
Enter your values to see the result.
Common mistake
Using cos θ instead of sin θ for this angle.
Limits
Straight conductor in a uniform field.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.