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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.
Symbol Meaning SI unit of measure magnetic vector potential: tesla meter (T⋅m) : area: square meter (m 2) : amplitude: meter: atomic mass number: unitless acceleration: meter per second squared (m/s 2)
The ampere is named for French physicist and mathematician André-Marie Ampère (1775–1836), who studied electromagnetism and laid the foundation of electrodynamics.In recognition of Ampère's contributions to the creation of modern electrical science, an international convention, signed at the 1881 International Exposition of Electricity, established the ampere as a standard unit of ...
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
where is the current, measured in amperes; is the potential difference, measured in volts; and is the resistance, measured in ohms. For alternating currents , especially at higher frequencies, skin effect causes the current to spread unevenly across the conductor cross-section, with higher density near the surface, thus increasing the apparent ...
The answer is that it does not matter: in the magnetostatic case, the current density is solenoidal (see next section), so the divergence theorem and continuity equation imply that the flux through any surface with boundary C, with the same sign convention, is the same. In practice, one usually chooses the most convenient surface (with the ...
where E is the electric field vector with units of volts per meter (analogous to V of Ohm's law which has units of volts), J is the current density vector with units of amperes per unit area (analogous to I of Ohm's law which has units of amperes), and ρ "rho" is the resistivity with units of ohm·meters (analogous to R of Ohm's law which has ...