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# IllustrationCurrent + time-dependent E-field generate a rotating B-field and vice versa

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This illustration is free to use with indication of the copyright: universaldenker.org

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:$\oint_{L} \boldsymbol{B} ~\cdot~ \text{d}\boldsymbol{l} ~=~ \mu_0 \, I + \int_{A} \frac{\partial \boldsymbol{E}}{\partial t} ~\cdot~ \text{d}\boldsymbol{a}$