[NOTES/EM-03011]-Summary of Maxwell's equations for Electrostatics

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Summary of Maxwell's equations for Electrostatics

Coulomb's law gives \begin{eqnarray} \nabla\cdot\bar{E}&=&\rho/\epsilon_0\\ \label{eq11} \nabla\times\bar{E}&=&0 \label{eq12} \end{eqnarray} Therefore; \begin{eqnarray} \nonumber\nabla\cdot\bar{E}=\rho/\epsilon_0 &\Longleftrightarrow& \text{Gauss law}\\ \nonumber\nabla\times\bar{E}=0 &\Longleftrightarrow& \text{Paths independent of work done by electrostatic forces}\\ \nonumber&\Longrightarrow&\text{Electrostatic forces are conservative} \end{eqnarray}