Editing Magnetism (section)

== Magnetic force ==
[[Image:Magnet0873.png|thumb|Magnetic lines of force of a bar magnet shown by iron filings on paper]]
[[File:Magnet bar.ogv|thumb|thumbtime=35|Detecting magnetic field with compass and with iron filings]]
{{main|Magnetic field}}

The phenomenon of magnetism is "mediated" by the magnetic field. An electric current or magnetic dipole creates a magnetic field, and that field, in turn, imparts magnetic forces on other particles that are in the fields.

Maxwell's equations, which simplify to the [[Biot–Savart law]] in the case of steady currents, describe the origin and behavior of the fields that govern these forces. Therefore, magnetism is seen whenever electrically [[electric charge|charged particles]] are in [[Motion (physics)|motion]]—for example, from movement of electrons in an [[electric current]], or in certain cases from the orbital motion of electrons around an atom's nucleus. They also arise from "intrinsic" [[magnetic dipole]]s arising from quantum-mechanical [[Spin (physics)|spin]].

The same situations that create magnetic fields—charge moving in a current or in an atom, and intrinsic magnetic dipoles—are also the situations in which a magnetic field has an effect, creating a force. Following is the formula for moving charge; for the forces on an intrinsic dipole, see magnetic dipole.

When a charged particle moves through a [[Magnetic field#B and H|magnetic field]] '''B''', it feels a [[Lorentz force]] '''F''' given by the [[cross product]]:<ref>{{cite book|first=John David|last=Jackson|author-link=John David Jackson (physicist)|title=Classical electrodynamics|edition=3rd|location=New York|publisher=[[John Wiley & Sons|Wiley]]|year=1999|isbn=978-0-471-30932-1}}</ref>
: <math>\mathbf{F} = q (\mathbf{v} \times \mathbf{B}) ,</math>
where
: <math>q</math> is the electric charge of the particle, and
: '''v''' is the [[velocity]] [[Vector (geometric)|vector]] of the particle

Because this is a [[cross product]], the force is [[perpendicular]] to both the motion of the particle and the magnetic field. The magnitude of the force is
: <math>F=qvB\sin\theta\,</math>
where <math>\theta</math> is the angle between '''v''' and '''B'''.

One tool for determining the direction of the velocity vector of a moving charge, the magnetic field, and the force exerted is labeling the [[index finger]] "V"{{Dubious|date=July 2021|reason=wrong if q is negative. "V" should be "qv".}}, the [[middle finger]] "B", and the [[thumb]] "F" with your right hand. When making a gun-like configuration, with the middle finger crossing under the index finger, the fingers represent the velocity vector, magnetic field vector, and force vector, respectively. See also [[right-hand rule]].