Question

What are Maxwell’s four integral equations

Answer 1

We may find on many textbooks what is resumed here as the four Maxwell's equations on the integral form:

• (Gauss’s law for electric fields) $\oint_S \vec{E}⋅\vec{dA}= \dfrac {q_{enc}}{ε_0}$

• (Gauss’s law for magnetic fields) $\oint_S \vec{B}⋅\vec{dA}=0$

• (Faraday’s law) $\oint_C \vec{E}⋅\vec{dl}= -\frac{d}{dt} \oint_S \vec{B}⋅\vec{dA}$

• (The Ampere–Maxwell law) $\oint_C \vec{B}⋅\vec{dl}= \mu_0( I_{enc}+ε_0\frac{d}{dt} \oint_S \vec{E}⋅\vec{dA} )$

Reference:

• Fleisch, D. (2008). A student's guide to Maxwell's equations. Cambridge University Press.
• Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage learning.