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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.
where this time is the charge density, is the current density vector, and is the current source-sink term. The current source and current sinks are where the current density emerges σ > 0 {\displaystyle \sigma >0} or vanishes σ < 0 {\displaystyle \sigma <0} , respectively (for example, the source and sink can represent the two poles of an ...
For example, the charge density at a point in a medium, which is a scalar in classical physics, must be combined with the local current density (a 3-vector) to comprise a relativistic 4-vector. Similarly, energy density must be combined with momentum density and pressure into the stress–energy tensor. Examples of scalar quantities in ...
vector field Momentum: p →: Product of an object's mass and velocity kg⋅m/s L M T −1: vector, extensive Pop: p →: Rate of change of crackle per unit time: the sixth time derivative of position m/s 6: L T −6: vector Pressure gradient: Pressure per unit distance pascal/m L −2 M 1 T −2: vector Temperature gradient
In the general case a conservation equation can be also a system of this kind of equations (a vector equation) in the form: [10]: 43 + = where y is called the conserved (vector) quantity, ∇y is its gradient, 0 is the zero vector, and A(y) is called the Jacobian of the current density. In fact as in the former scalar case, also in the vector ...
For spatial density, current, current density and flux, the notations are common from one context to another, differing only by a change in subscripts. For current density, t ^ {\displaystyle \mathbf {\hat {t}} } is a unit vector in the direction of flow, i.e. tangent to a flowline.
where E is the electric field vector with units of volts per meter (analogous to V of Ohm's law which has units of volts), J is the current density vector with units of amperes per unit area (analogous to I of Ohm's law which has units of amperes), and ρ "rho" is the resistivity with units of ohm·meters (analogous to R of Ohm's law which has ...
For vector flux, the surface integral of j over a surface S, gives the proper flowing per unit of time through the surface: = ^ =, where A (and its infinitesimal) is the vector area – combination = ^ of the magnitude of the area A through which the property passes and a unit vector ^ normal to the area. Unlike in the second set of equations ...