The 4 Maxwell Equations in Vacuum
Simple explanation of the Maxwell's equations for beginners. The divergence integral and the curl integral theorems are also explained.
Illustration Current + time-dependent E-field generate a rotating B-field and vice versa
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A time-varying electric field \( \boldsymbol{E}(t) \) and/or a constant electric current \(I\) through a surface \(A\) create a time-dependent magnetic field \( \boldsymbol{B}(t) \) which forms a vortex along the edge of the surface \(A\). This can be summarized in the following 4th Maxwell equation in integral form:\[ \oint_{L} \boldsymbol{B} ~\cdot~ \text{d}\boldsymbol{l} ~=~ \mu_0 \, I + \int_{A} \frac{\partial \boldsymbol{E}}{\partial t} ~\cdot~ \text{d}\boldsymbol{a} \]
