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In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law) [1] relates the circulation of a magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell derived it using hydrodynamics in his 1861 published paper "On Physical Lines of Force". [2]
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 ...
This is related to a certain limited kind of redundancy in Maxwell's equations: It can be proven that any system satisfying Faraday's law and Ampère's circuital law automatically also satisfies the two Gauss's laws, as long as the system's initial condition does, and assuming conservation of charge and the nonexistence of magnetic monopoles.
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 ...
It is valid in the magnetostatic approximation and consistent with both Ampère's circuital law and Gauss's law for magnetism. [2] When magnetostatics does not apply, the Biot–Savart law should be replaced by Jefimenko's equations. The law is named after Jean-Baptiste Biot and Félix Savart, who discovered this relationship in 1820.
He added the displacement current term to Ampère's circuital law and this enabled him to derive the electromagnetic wave equation in his later 1865 paper A Dynamical Theory of the Electromagnetic Field and to demonstrate the fact that light is an electromagnetic wave. This fact was later confirmed experimentally by Heinrich Hertz in 1887.
November 22, 2024 at 12:04 AM If you’re stuck on today’s Wordle answer, we’re here to help—but beware of spoilers for Wordle 1252 ahead. Let's start with a few hints.
Applying Ampère's circuital law to the solenoid (see figure on the right) gives us B l = μ 0 N I , {\displaystyle Bl=\mu _{0}NI,} where B {\displaystyle B} is the magnetic flux density , l {\displaystyle l} is the length of the solenoid, μ 0 {\displaystyle \mu _{0}} is the magnetic constant , N {\displaystyle N} the number of turns, and I ...