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Media related to Ampere's law at Wikimedia Commons; MISN-0-138 Ampere's Law by Kirby Morgan for Project PHYSNET. MISN-0-145 The Ampere–Maxwell Equation; Displacement Current (PDF file) by J. S. Kovacs for Project PHYSNET. A Dynamical Theory of the Electromagnetic Field Maxwell's paper of 1864
In magnetostatics, the force of attraction or repulsion between two current-carrying wires (see first figure below) is often called Ampère's force law. The physical origin of this force is that each wire generates a magnetic field , following the Biot–Savart law , and the other wire experiences a magnetic force as a consequence, following ...
Maxwell added displacement current to the electric current term in Ampère's circuital law. In his 1865 paper A Dynamical Theory of the Electromagnetic Field Maxwell used this amended version of Ampère's circuital law to derive the electromagnetic wave equation. This derivation is now generally accepted as a historical landmark in physics by ...
Importantly, Gauss's force law is a significant generalization of Ampere's force law, since moving point charges do not represent direct currents. In fact, today Ampere's force law is no longer presented in its original form, as there are equivalent representations for direct currents such as the Biot-Savart law in combination with the Lorentz ...
André-Marie Ampère (UK: / ˈ æ m p ɛər /, US: / ˈ æ m p ɪər /; [1] French: [ɑ̃dʁe maʁi ɑ̃pɛʁ]; 20 January 1775 – 10 June 1836) [2] was a French physicist and mathematician who was one of the founders of the science of classical electromagnetism, which he referred to as electrodynamics.
The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems.
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Maxwell's equations can directly give inhomogeneous wave equations for the electric field E and magnetic field B. [1] Substituting Gauss's law for electricity and Ampère's law into the curl of Faraday's law of induction, and using the curl of the curl identity ∇ × (∇ × X) = ∇(∇ ⋅ X) − ∇ 2 X (The last term in the right side is the vector Laplacian, not Laplacian applied on ...