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$$\begin{array}{|c|c|} \hline\textrm{True in Statics} &\textrm{True in General}\\ \hline \mathbf F = \mathbf E~= \dfrac1{4\pi\varepsilon_o}~ \dfrac{q_1q_2}{r^2}~\mathbf{\hat r} & \mathbf F= q(\mathbf E+ \mathbf v\times \mathbf B)\\ \hline \nabla \cdot \mathbf E = \dfrac{\rho}{\varepsilon_0} & \nabla \cdot \mathbf E = \dfrac{\rho}{\varepsilon_0} \\ \hline \nabla\times \mathbf E= \mathbf 0& \nabla \times \mathbf E = ~\partial_t\mathbf B\\ \hline \mathbf E= -\nabla\varphi & \mathbf E= -\nabla \varphi - \partial_t \mathbf A\\ \hline \nabla^2\varphi = -\dfrac{\rho}{\varepsilon_0} & \nabla^2\varphi -\dfrac1 {c^2}\partial^2_t\varphi = -\dfrac\rho{\varepsilon_0}\\ \hline \varphi(\mathbf 1)= \dfrac1{4\pi\varepsilon_0}\displaystyle\int\dfrac{\rho(\mathbf 2)}{r_{12}}~\mathrm dV_2 & \varphi(\mathbf 1, t)= \dfrac{1}{4\pi\varepsilon_0}\displaystyle \int \dfrac{\rho(\mathrm 2, t')}{r_{12}}~\mathrm dV_2\\ U= \dfrac12 \left(\displaystyle\int \rho\varphi~\mathrm dV + \displaystyle \int \mathbf J\cdot \mathbf A~\mathrm dV\right) & U= \dfrac{\varepsilon_0}2 \left(\displaystyle\int \varepsilon_0~\mathbf E\cdot \mathbf E + {c^2}\displaystyle\int \mathbf B\cdot \mathbf B~\mathrm dV\right)\\ \hline\end{array}$$