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]
\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}),
where
F is the force (in newtons)
E is the electric field (in volts per metre)
B is the magnetic field (in teslas)
q is the electric charge of the particle (in coulombs)
v is the instantaneous velocity of the particle (in metres per second)
× is the vector cross product
or equivalently the following equation in terms of the vector potential and scalar potential:
\mathbf{F} = q ( - \nabla \phi - \frac { \partial \mathbf{A} } { \partial t } + \mathbf{v} \times (\nabla \times \mathbf{A})),
where:
∇ and ∇ × are gradient and curl, respectively
A and ɸ are the magnetic vector potential and electrostatic potential, respectively, which are related to E and B by[2]
\mathbf{E} = - \nabla \phi - \frac { \partial \mathbf{A} } { \partial t }
\mathbf{B} = \nabla \times \mathbf{A}.
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]
\mathbf{F}_{mag} = q(\mathbf{v} \times \mathbf{B})
