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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:
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 ...
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.
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 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 ...
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.
In modern terminology, the conserved quantity is called the Noether charge, while the flow carrying that charge is called the Noether current. The Noether current is defined up to a solenoidal (divergenceless) vector field. In the context of gravitation, Felix Klein's statement of Noether's theorem for action I stipulates for the invariants: [7]
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.