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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 ...
Electric current can be directly measured with a galvanometer, but this method involves breaking the electrical circuit, which is sometimes inconvenient. Current can also be measured without breaking the circuit by detecting the magnetic field associated with the current. Devices, at the circuit level, use various techniques to measure current:
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.
For every scalar function of position and time λ(x, t), the potentials can be changed by a gauge transformation as ′ =, ′ = + without changing the electric and magnetic field. Two pairs of gauge transformed potentials ( φ , A ) and ( φ ′, A ′) are called gauge equivalent , and the freedom to select any pair of potentials in its gauge ...
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.
As seen in the figure, the current does not increase linearly with applied voltage for a diode. One can determine a value of current (I) for a given value of applied voltage (V) from the curve, but not from Ohm's law, since the value of "resistance" is not constant as a function of applied voltage. Further, the current only increases ...
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scalar Electrical conductivity: σ: 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 ...