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IllustrationTime changing magnetic field generates a rotating electric field and vice versa

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Time variation of the magnetic field $$\boldsymbol{B}$$ or the time variation of the surface $$A$$ penetrated by magnetic field $$\boldsymbol{B}$$ generates an electric field $$\boldsymbol{E}$$ along the edge of the surface $$A$$, which can lead to an electric current. This experimental finding is called the law of induction and is mathematically summarized in the fourth Maxwell equation (if $$A$$ is kept constant):$\nabla \times \boldsymbol{E} ~=~ - \frac{\partial \boldsymbol{B}}{\partial t}$

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