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As of the 2019 revision of the SI, the ampere is defined by fixing the elementary charge e to be exactly 1.602 176 634 × 10 −19 C, [6] [9] which means an ampere is an electric current equivalent to 10 19 elementary charges moving every 1.602 176 634 seconds or 6.241 509 074 × 10 18 elementary charges moving in a second.
In a linear, macroscopic theory, the influence of matter on the electromagnetic field is described through more general linear transformation in the space of 2-forms. We call : the constitutive transformation. The role of this transformation is comparable to the Hodge duality transformation.
Ampère began developing a mathematical and physical theory to understand the relationship between electricity and magnetism. Furthering Ørsted's experimental work, Ampère showed that two parallel wires carrying electric currents attract or repel each other, depending on whether the currents flow in the same or opposite directions ...
Ampère's electrodynamics: analysis of the meaning and evolution of Ampère's force between current elements, together with a complete translation of his masterpiece: Theory of electrodynamic phenomena, uniquely deduced from experience (PDF). Montreal: Apeiron. ISBN 978-1-987980-03-5. Maxwell's 1873 derivation:
The publication of the equations marked the unification of a theory for previously separately described phenomena: magnetism, electricity, light, and associated radiation. Since the mid-20th century, it has been understood that Maxwell's equations do not give an exact description of electromagnetic phenomena, but are instead a classical limit ...
In the 1850s Scottish mathematical physicist James Clerk Maxwell generalized these results and others into a single mathematical law. The original form of Maxwell's circuital law, which he derived as early as 1855 in his paper "On Faraday's Lines of Force" [ 9 ] based on an analogy to hydrodynamics, relates magnetic fields to electric currents ...
ampere (A) moment of inertia: kilogram meter squared (kg⋅m 2) intensity: watt per square meter (W/m 2) imaginary unit: unitless electric current: ampere (A) ^ Cartesian x-axis basis unit vector unitless current density: ampere per square meter (A/m 2) impulse
Theory of functions of a complex variable, the historical name for complex analysis, the branch of mathematical analysis that investigates functions of complex numbers; Constructive function theory, the study of the connection between the smoothness of a function and its degree of approximation