Maxwell’s Equations 2

Use the vector identity: $\nabla \cdot \left( \nabla \times \overline{A} \right) = 0$

From this:

(1) $\begin{equation*} \nabla \cdot \left( \nabla \times \overline{E} \right) = 0 = -\left( \nabla \cdot \frac{\partial B}{\partial t} \right) = -\frac{\partial}{\partial t} \left(\nabla \cdot \overline{B} \right) \rightarrow \nabla \cdot \overline{B} = 0 \end{equation*}$

Following this method:

(2) $\begin{equation*} \nabla \cdot \left( \overline{J} + \frac{\partial D}{\partial t} \right) = \nabla \cdot \overline{J} + \nabla \cdot \frac{\partial \overline{D}}{\partial t} = \nabla \cdot \overline{J} + \frac{\partial}{\partial t} \left( \nabla \cdot \overline{D} \right) \end{equation*}$

That’s good for now …

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