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In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. [1] The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point.
In the production of the Lorentz force, the difference between electric fields and magnetic fields is that a force from a magnetic field on a charged particle is generally due to the charged particle's movement, [3] while the force imparted by an electric field on a charged particle is not due to the charged particle's movement. This may be ...
One difference between the Gaussian and SI systems is in the factor 4π in various formulas that relate the quantities that they define. With SI electromagnetic units, called rationalized, [3] [4] Maxwell's equations have no explicit factors of 4π in the formulae, whereas the inverse-square force laws – Coulomb's law and the Biot–Savart law – do have a factor of 4π attached to the r 2.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Here E and D are the electric field and displacement field, respectively, B and H are the magnetic fields, P is the polarization density, M is the magnetization, ρ is charge density, J is current density, c is the speed of light in vacuum, ϕ is the electric potential, A is the magnetic vector potential, F is the Lorentz force acting on a body ...
In the CGS system, the unit of the H-field is the oersted and the unit of the B-field is the gauss.In the SI system, the unit ampere per meter (A/m), which is equivalent to newton per weber, is used for the H-field and the unit of tesla is used for the B-field.
The charge density appears in the continuity equation for electric current, and also in Maxwell's Equations. It is the principal source term of the electromagnetic field; when the charge distribution moves, this corresponds to a current density. The charge density of molecules impacts chemical and separation processes.
The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems.