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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]
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 ...
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 ampere is an SI base unit and electric ... Ohm's law states that the current through a conductor between ... 20 The commonly known SI unit of power, ...
Without the displacement current term Ampere's law would give zero magnetic field for this surface. Therefore, without the displacement current term Ampere's law gives inconsistent results, the magnetic field would depend on the surface chosen for integration.
Maxwell's equations on a plaque on his statue in Edinburgh. Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits.
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 ...
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 n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.