How to use the Magnetic Force on a Current-Carrying Wire Calculator
A current-carrying wire placed in a magnetic field experiences a force because the field pushes on every moving charge inside the conductor. Summed over a straight wire of length L, this gives the standard result F = B I L sin(θ), where B is the magnetic flux density (in teslas), I is the current (in amps), L is the length of wire inside the field (in meters), and θ is the angle between the current direction and the field lines. Enter those four values below to get the force, the force per unit length, the maximum force the same wire could feel, and the fraction of that maximum you're actually getting at your angle.
Deriving F = BIL sin(θ)
Each charge carrier moving inside the wire feels a Lorentz force. Summing that force over every carrier in a straight wire of length L carrying current I gives the vector result F = I L × B, the cross product of the current-length vector and the magnetic field vector. Taking the magnitude gives F = BIL sin(θ), since |A × B| = |A||B| sin(θ) for any two vectors. The direction of F is always perpendicular to both the wire and the field, found with the right-hand rule: point your fingers along the current, curl them toward B, and your thumb points along F.
Reading the angle and the special cases
θ is measured between the current direction and the magnetic field vector, not between the wire and some fixed axis. At θ = 90° (wire perpendicular to the field) sin(θ) = 1 and the wire feels the maximum possible force, F_max = BIL. At θ = 0° or 180° (wire parallel or antiparallel to the field) sin(θ) = 0 and the wire feels no magnetic force at all, even though current is still flowing. Most textbook problems and lab setups use θ = 90° by default because that configuration produces the largest, easiest-to-measure force.
Where this shows up in practice
- Electric motors: current-carrying windings sit inside a magnetic field, so F = BIL sin(θ) becomes the torque-producing force that spins the rotor.
- Loudspeakers: the voice coil sits in a permanent magnet's field; the audio current through it produces the force that moves the cone back and forth.
- Busbars and rail systems: high-current conductors near other current-carrying parts feel real mechanical forces (F/L = BI sin(θ)) that engineers must brace for during fault currents.
- Galvanometers and ammeters: the same force law, applied to a coil instead of a single straight wire, is what deflects the needle.