Ampère–Maxwell Law

\[\nabla \times \mathbf{B}=\mu_{0}\mathbf{J}+\mu_{0}\varepsilon_{0}\frac{ \partial \mathbf{E} }{ \partial t }\] \[\displaystyle\oint_{\text{loop}}\mathbf{B}\cdot d\mathbf{l}=\mu_{0}I_{\text{enclosed}}+\mu_{0}\varepsilon_{0} \frac{d\Phi_{E}}{dt}\]

Magnetic fields are produced by electric currents and by changing electric flux.

The first term is ordinary electromagnetism (currents make magnetic fields). The second term (Maxwell’s correction) shows that even without a physical current, a changing electric field also creates a magnetic field (essential for electromagnetic waves).

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Notes mentioning this note

Maxwell's Equations
[[Gauss’s Law for Electricity]] The electric flux out of a closed surface is proportional to the total electric charge enclosed....

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