MaxwellAmpèreGleichung

The MaxwellAmpèreGleichung, also known as Ampère's Law with Maxwell's addition, is one of the four fundamental equations of electromagnetism that form Maxwell's equations. It describes how electric currents and changing electric fields create magnetic fields. The original Ampère's Law stated that a magnetic field is generated by an electric current. Maxwell's crucial contribution was adding a term to account for the fact that a changing electric field, even in the absence of a current, also produces a magnetic field. This addition, known as the displacement current, was essential for Maxwell's unification of electricity and magnetism and for predicting the existence of electromagnetic waves. Mathematically, the equation relates the curl of the magnetic field to the electric current density and the time rate of change of the electric displacement field. It is a cornerstone of classical electrodynamics, underpinning much of our understanding of electromagnetism, including the behavior of light and radio waves. Without Maxwell's addition, the equations would not be self-consistent and would not predict wave propagation. The MaxwellAmpèreGleichung is a vector equation and is often expressed in integral or differential form.