Editing Lorentz force (section)

== Force on a current-carrying wire ==
{{see also|Electric motor#Force and torque|Biot–Savart law}}
[[File:Regla mano derecha Laplace.svg|right|thumb|Right-hand rule for a current-carrying wire in a magnetic field {{mvar|B}}]]
When a wire carrying an electric current is placed in an external magnetic field, each of the moving charges, which comprise the current, experiences the Lorentz force, and together they can create a macroscopic force on the wire (sometimes called the '''Laplace force'''). By combining the Lorentz force law above with the definition of electric current, the following equation results, in the case of a straight stationary wire in a homogeneous field:{{sfn|Purcell|Morin|2013|p=284}}
<math display="block">\mathbf{F} = I \boldsymbol{\ell} \times \mathbf{B} ,</math>
where {{math|'''ℓ'''}} is a vector whose magnitude is the length of the wire, and whose direction is along the wire, aligned with the direction of the [[conventional current]] {{mvar|I}}.

If the wire is not straight, the force on it can be computed by applying this formula to each [[infinitesimal]] segment of wire <math> \mathrm d \boldsymbol \ell </math>, then adding up all these forces by [[integration (calculus)|integration]]. This results in the same formal expression, but {{math|'''ℓ'''}} should now be understood as the vector connecting the end points of the curved wire with direction from starting to end point of conventional current. Usually, there will also be a net [[torque]].

If, in addition, the magnetic field is inhomogeneous, the net force on a stationary rigid wire carrying a steady current {{mvar|I}} is given by integration along the wire,{{sfn|Griffiths|2023|p=216}}
<math display="block">\mathbf{F} = I\int (\mathrm{d}\boldsymbol{\ell}\times \mathbf{B}).</math>
One application of this is [[Ampère's force law]], which describes how two current-carrying wires can attract or repel each other, since each experiences a Lorentz force from the other's generated magnetic field.

Another application is an [[induction motor]]. The stator winding AC current generates a moving magnetic field which induces a current in the rotor. The subsequent Lorentz force <math>\mathbf{F}</math> acting on the rotor creates a torque, making the motor spin. Hence, though the Lorentz force law does not apply when the magnetic field <math>\mathbf{B}</math> is generated by the current <math>I</math>, it does apply when the current <math>I</math> is induced by the movement of magnetic field <math>\mathbf{B}</math>.