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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.
A scalar in physics and other areas of science is also a scalar in mathematics, as an element of a mathematical field used to define a vector space.For example, the magnitude (or length) of an electric field vector is calculated as the square root of its absolute square (the inner product of the electric field with itself); so, the inner product's result is an element of the mathematical field ...
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
For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. [1]
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 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 ...
A scalar field is a tensor field of order zero, [3] and the term "scalar field" may be used to distinguish a function of this kind with a more general tensor field, density, or differential form. The scalar field of sin ( 2 π ( x y + σ ) ) {\displaystyle \sin(2\pi (xy+\sigma ))} oscillating as σ {\displaystyle \sigma } increases.
In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [ 1 ] [ 2 ] It is typically formulated as the product of a unit of measurement and a vector numerical value ( unitless ), often a Euclidean vector with magnitude and direction .