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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 ...
A field can be classified as a scalar field, a vector field, a spinor field or a tensor field according to whether the represented physical quantity is a scalar, a vector, a spinor, or a tensor, respectively. A field has a consistent tensorial character wherever it is defined: i.e. a field cannot be a scalar field somewhere and a vector field ...
Measure of a material's ability to conduct an electric current S/m L −3 M −1 T 3 I 2: scalar Electric potential: φ: Energy required to move a unit charge through an electric field from a reference point volt (V = J/C) L 2 M T −3 I −1: extensive, scalar Electrical resistance: R: Electric potential per unit electric current ohm (Ω = V/A ...
In classical electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by V or occasionally φ, [1] equal to the electric potential energy of any charged particle at any location (measured in joules) divided by the charge of that particle (measured ...
Example: The vector field ... the resulting vector field is the electric field. ... expressed as their scalar products. For example, given a particle in a force field ...
Mathematically, a scalar field on a region U is a real or complex-valued function or distribution on U. [1] [2] The region U may be a set in some Euclidean space, Minkowski space, or more generally a subset of a manifold, and it is typical in mathematics to impose further conditions on the field, such that it be continuous or often continuously differentiable to some order.
A free vector is a vector quantity having an undefined support or region of application; it can be freely translated with no consequences; a displacement vector is a prototypical example of free vector. Aside from the notion of units and support, physical vector quantities may also differ from Euclidean vectors in terms of metric.
In advanced classical mechanics it is often useful, and in quantum mechanics frequently essential, to express Maxwell's equations in a potential formulation involving the electric potential (also called scalar potential) φ, and the magnetic potential (a vector potential) A. For example, the analysis of radio antennas makes full use of Maxwell ...