Editing Magnetic field (section)

====Force on a charged particle====
{{Main|Lorentz force}}

A [[charged particle]] moving in a {{math|'''B'''}}-field experiences a ''sideways'' force that is proportional to the strength of the magnetic field, the component of the velocity that is perpendicular to the magnetic field and the charge of the particle. This force is known as the ''Lorentz force'', and is given by
<math display="block">\mathbf{F} = q\mathbf{E} + q \mathbf{v} \times \mathbf{B},</math>
where {{math|'''F'''}} is the [[force]], {{math|''q''}} is the [[electric charge]] of the particle, {{math|'''v'''}} is the instantaneous [[velocity]] of the particle, and {{math|'''B'''}} is the magnetic field (in [[tesla (unit)|teslas]]).

The Lorentz force is always perpendicular to both the velocity of the particle and the magnetic field that created it. When a charged particle moves in a static magnetic field, it traces a helical path in which the helix axis is parallel to the magnetic field, and in which the speed of the particle remains constant. Because the magnetic force is always perpendicular to the motion, the magnetic field can do no [[mechanical work|work]] on an isolated charge.<ref>{{Cite web|title=K. McDonald's Physics Examples - Disk|url=https://puhep1.princeton.edu/~kirkmcd/examples/disk.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://puhep1.princeton.edu/~kirkmcd/examples/disk.pdf |archive-date=2022-10-09 |url-status=live|access-date=2021-02-13|website=puhep1.princeton.edu}}</ref><ref>{{Cite web|title=K. McDonald's Physics Examples - Railgun|url=https://physics.princeton.edu//~mcdonald/examples/railgun.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://physics.princeton.edu//~mcdonald/examples/railgun.pdf |archive-date=2022-10-09 |url-status=live | access-date=2021-02-13|website=puhep1.princeton.edu}}</ref> It can only do work indirectly, via the electric field generated by a changing magnetic field. It is often claimed that the magnetic force can do work to a non-elementary [[magnetic dipole]], or to charged particles whose motion is constrained by other forces, but this is incorrect<ref name=Deissler>
{{cite journal
 |last = Deissler | first = R.J.
 |year=2008
 |title=Dipole in a magnetic field, work, and quantum spin
 |url=http://academic.csuohio.edu/deissler/PhysRevE_77_036609.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://academic.csuohio.edu/deissler/PhysRevE_77_036609.pdf |archive-date=2022-10-09 |url-status=live
 |journal=[[Physical Review E]]
 |volume=77 |issue=3, pt 2
 |page=036609
 |pmid=18517545
 |doi=10.1103/PhysRevE.77.036609
 |bibcode = 2008PhRvE..77c6609D }}</ref> because the work in those cases is performed by the electric forces of the charges deflected by the magnetic field.