Force on current-carrying wire

           Force on current-carrying wire

A straight, stationary wire carrying an electric current, when placed in an external magnetic field, feels a force. This force is the result of the Lorentz force (see above) acting on each electron (or any other charge carrier) moving in the wire. The formula for the total force is as follows:

where

F = Force, measured in newtons

I = current in wire, measured in amperes

B = magnetic field vector, measured in teslas

    = vector cross product

L = a vector, whose magnitude is the length of wire (measured in metres), and whose direction is along the wire, aligned with the direction of conventional current flow.

Alternatively, some authors write

where the vector direction is now associated with the current variable, instead of the length variable. The two forms are equivalent

If the wire is not straight but curved, the force on it can be computed by applying this formula to each infinitesimal segment of wire, then adding up all these forces via integration.

The Lorentz force on a macroscopic current is often referred to as the Laplace force.