$$\begin{array}{|c|c|} \hline\textrm{True in Statics} &\textrm{True in General}\\ \hline \mathbf F = \mathbf E~= \dfrac1{4\pi\varepsilon_o}~ \dfrac{q_1q_2}{r^2}~\mathbf{\hat r} & \mathbf F= q(\mathbf E+ \mathbf v\times \mathbf B)\\ \hline \nabla \cdot \mathbf E = \dfrac{\rho}{\varepsilon_0} & \nabla \cdot \mathbf E = \dfrac{\rho}{\varepsilon_0} \\ \hline \nabla\times \mathbf E= \mathbf 0& \nabla \times \mathbf E = ~-\partial_t\mathbf B\\ \hline \mathbf E= -\nabla\varphi & \mathbf E= -\nabla \varphi - \partial_t \mathbf A\\ \hline \nabla^2\varphi = -\dfrac{\rho}{\varepsilon_0} & \nabla^2\varphi -\dfrac1 {c^2}\partial^2_t\varphi = -\dfrac\rho{\varepsilon_0}\\ \hline \varphi(\mathbf 1)= \dfrac1{4\pi\varepsilon_0}\displaystyle\int\dfrac{\rho(\mathbf 2)}{r_{12}}~\mathrm dV_2 & \varphi(\mathbf 1, t)= \dfrac{1}{4\pi\varepsilon_0}\displaystyle \int \dfrac{\rho(\mathbf 2, t^\prime)}{r_{12}}~\mathrm dV_2\\\hline U= \dfrac12 \left(\displaystyle\int \rho\varphi~\mathrm dV \right) & U= \dfrac{\varepsilon_0}2 \left(\displaystyle\int \mathbf E\cdot \mathbf E~\mathrm dV + {c^2}\displaystyle\int \mathbf B\cdot \mathbf B~\mathrm dV\right)\\ \hline\end{array}$$$$\begin{array}{|c|c|} \hline\textrm{True in Statics} &\textrm{True in General}\\ \hline \mathbf F ~= \dfrac1{4\pi\varepsilon_o}~ \dfrac{q_1q_2}{r^2}~\mathbf{\hat r} & \mathbf F= q(\mathbf E+ \mathbf v\times \mathbf B)\\ \hline \nabla \cdot \mathbf E = \dfrac{\rho}{\varepsilon_0} & \nabla \cdot \mathbf E = \dfrac{\rho}{\varepsilon_0} \\ \hline \nabla\times \mathbf E= \mathbf 0& \nabla \times \mathbf E = ~-\partial_t\mathbf B\\ \hline \mathbf E= -\nabla\varphi & \mathbf E= -\nabla \varphi - \partial_t \mathbf A\\ \hline \nabla^2\varphi = -\dfrac{\rho}{\varepsilon_0} & \nabla^2\varphi -\dfrac1 {c^2}\partial^2_t\varphi = -\dfrac\rho{\varepsilon_0}\\ \hline \varphi(\mathbf 1)= \dfrac1{4\pi\varepsilon_0}\displaystyle\int\dfrac{\rho(\mathbf 2)}{r_{12}}~\mathrm dV_2 & \varphi(\mathbf 1, t)= \dfrac{1}{4\pi\varepsilon_0}\displaystyle \int \dfrac{\rho(\mathbf 2, t^\prime)}{r_{12}}~\mathrm dV_2\\\hline U= \dfrac12 \left(\displaystyle\int \rho\varphi~\mathrm dV \right) & U= \dfrac{\varepsilon_0}2 \left(\displaystyle\int \mathbf E\cdot \mathbf E~\mathrm dV + {c^2}\displaystyle\int \mathbf B\cdot \mathbf B~\mathrm dV\right)\\ \hline\end{array}$$
where
\begin{align}\mathbf F& \equiv \textrm{Total force},\\ \mathbf E& \equiv \textrm{Electric field},\\ \mathbf B &\equiv \textrm{Magnetic field},\\ \nabla &\equiv \textrm{del operator},\\ \rho &\equiv\textrm{Charge-density},\\ \varphi &\equiv \textrm{Scalar-potential},\\ \mathbf A &\equiv \textrm{Vector-potential},\\ \partial_t &\equiv \dfrac{\partial}{\partial t},\\ \nabla^2 &\equiv \textrm{Lapalacian operator},\\ \partial^2_t &\equiv \dfrac{\partial^2}{\partial t^2},\\ U &\equiv \textrm{Potential-energy}, \\ t^\prime &\equiv \textrm{retarded-time} = t-\dfrac{r_{12}}c\;. \end{align}