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A scalar is an element of a field which is used to define a vector space.In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector.
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 ...
An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. [1]: 2 [2]: 622 The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor.
However, the variables are generalized to complex numbers and the current and voltage waveforms are complex exponentials. [ 29 ] In this approach, a voltage or current waveform takes the form Ae st , where t is time, s is a complex parameter, and A is a complex scalar.
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.
In physics, action is a scalar quantity that describes how the balance of kinetic versus potential energy of a physical system changes with trajectory. Action is significant because it is an input to the principle of stationary action, an approach to classical mechanics that is simpler for multiple objects. [1]
Given a current such as electric current—charge per time, current density would also be a flux according to the transport definition—charge per time per area. Due to the conflicting definitions of flux , and the interchangeability of flux , flow , and current in nontechnical English, all of the terms used in this paragraph are sometimes ...
Scalar control of an AC electrical motor is a way to achieve the variable speed operation by manipulating the supply voltage or current ("magnitude") and the supply frequency while ignoring the magnetic field orientation inside the motor. [1]