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The net electric current I is the surface integral of the electric current density J passing through Σ: =, where dS denotes the differential vector element of surface area S, normal to surface Σ. (Vector area is sometimes denoted by A rather than S , but this conflicts with the notation for magnetic vector potential ).
The ampere is an SI base unit and electric current is a base quantity in the International System of Quantities (ISQ). [4]: 15 Electric current is also known as amperage and is measured using a device called an ammeter. [2]: 788 Electric currents create magnetic fields, which are used in motors, generators, inductors, and transformers.
The current entering any junction is equal to the current leaving that junction. i 2 + i 3 = i 1 + i 4. This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node; or equivalently:
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 nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
The most common description of the electromagnetic field uses two three-dimensional vector fields called the electric field and the magnetic field.These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates.
A continuity equation is the mathematical way to express this kind of statement. For example, the continuity equation for electric charge states that the amount of electric charge in any volume of space can only change by the amount of electric current flowing into or out of that volume through its boundaries.
A current such that M(T) < ∞ is representable by integration of a regular Borel measure by a version of the Riesz representation theorem. This is the starting point of homological integration . An intermediate norm is Whitney's flat norm , defined by F ( T ) := inf { M ( T − ∂ A ) + M ( A ) : A ∈ E m + 1 } . {\displaystyle \mathbf {F ...
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.