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Faraday's law of induction was suggestive to Einstein when he wrote in 1905 about the "reciprocal electrodynamic action of a magnet and a conductor". [ 15 ] Nevertheless, the aspiration, reflected in references for this article, is for an analytic geometry of spacetime and charges providing a deductive route to forces and currents in practice.
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.
The Feynman Lectures on Physics (vol. 2, ch. 13–6) uses this method to derive the magnetic force on charge in parallel motion next to a current-carrying wire. See also Haskell [8] and Landau. [9] If the charge instead moves perpendicular to a current-carrying wire, electrostatics cannot be used to derive the magnetic force.
A separate law of nature, the Lorentz force law, describes how the electric and magnetic fields act on charged particles and currents. By convention, a version of this law in the original equations by Maxwell is no longer included. The vector calculus formalism below, the work of Oliver Heaviside, [6] [7] has become standard.
Formulas for physical laws of electromagnetism (such as Maxwell's equations) need to be adjusted depending on what system of units one uses. This is because there is no one-to-one correspondence between electromagnetic units in SI and those in CGS, as is the case for mechanical units.
The Biot–Savart law [4]: Sec 5-2-1 is used for computing the resultant magnetic flux density B at position r in 3D-space generated by a filamentary current I (for example due to a wire). A steady (or stationary) current is a continual flow of charges which does not change with time and the charge neither accumulates nor depletes at any point.
The Maxwell stress tensor (named after James Clerk Maxwell) is a symmetric second-order tensor in three dimensions that is used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum.
Informally, the case of a point charge in an arbitrary static electric field is a simple consequence of Gauss's law.For a particle to be in a stable equilibrium, small perturbations ("pushes") on the particle in any direction should not break the equilibrium; the particle should "fall back" to its previous position.