# Lorentz force

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In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:[1]

where

or equivalently the following equation in terms of the vector potential and scalar potential:

where:

Note that these are vector equations: All the quantities written in boldface are vectors (in particular, F, E, v, B, A).

The Lorentz force law has a close relationship with Faraday's law of induction.

A positively charged particle will be accelerated in the same linear orientation as the E field, but will curve perpendicularly to both the instantaneous velocity vector v and the B field according to the right-hand rule (in detail, if the thumb of the right hand points along v and the index finger along B, then the middle finger points along F).

The term qE is called the electric force, while the term qv × B is called the magnetic force.[3] According to some definitions, the term "Lorentz force" refers specifically to the formula for the magnetic force:[4]

with the total electromagnetic force (including the electric force) given some other (nonstandard) name. This article will not follow this nomenclature: In what follows, the term "Lorentz force" will refer only to the expression for the total force.

The magnetic force component of the Lorentz force manifests itself as the force that acts on a current-carrying wire in a magnetic field. In that context, it is also called the Laplace force. The magnitude of this magnetic force is q v B sin θ and direction is perpendicular to the plane formed by v and B. If the particle moves perpendicular to the field, the magnitude becomes q v B and the trajectory of the particle will be circular. Also the force is in the direction perpendicular to the velocity, so magnitude of velocity will not change, i.e. the motion will be uniform circular motion.

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