I assume you either defined it in the beginning of your document or you use a document class that specifies it itself accordingly. Anyhow, you can use the chngcntr
package to manually define how the counting is done.
Here an MWE with the numbering done without the section number:
\documentclass[12pt]{article}
\usepackage{chngcntr}
\counterwithout{equation}{section}
\begin{document}
\section{Section One}
This is some text in Section 1.
\section{Section Two}
This is some text in Section 2. And here comes your equation:
\begin{equation}
\overrightarrow { \rm \nabla } \cdot [\varepsilon \overrightarrow{ \rm (r)} \nabla \varphi \overrightarrow{ \rm (r) }] = - \frac{1}{\varepsilon_0} \left [ \rho^{fixed} \overrightarrow{ \rm (r) } + e \sum_{i}^{n} C_{i}^{b} exp ( - \frac{ez_i}{kT} \varphi \overrightarrow{ \rm (r) } ) \right ]
\end{equation}
\end{document}
And here an MWE with the numbering done with the section number:
\documentclass[12pt]{article}
\usepackage{chngcntr}
\counterwithin{equation}{section}
\begin{document}
\section{Section One}
This is some text in Section 1.
\section{Section Two}
This is some text in Section 2. And here comes your equation:
\begin{equation}
\overrightarrow { \rm \nabla } \cdot [\varepsilon \overrightarrow{ \rm (r)} \nabla \varphi \overrightarrow{ \rm (r) }] = - \frac{1}{\varepsilon_0} \left [ \rho^{fixed} \overrightarrow{ \rm (r) } + e \sum_{i}^{n} C_{i}^{b} exp ( - \frac{ez_i}{kT} \varphi \overrightarrow{ \rm (r) } ) \right ]
\end{equation}
\end{document}
\rm
has not been defined in latex by default since 1993.\documentclass{article} \begin{document} \begin{equation} \overrightarrow { \rm \nabla } \cdot [\varepsilon \overrightarrow{ \rm (r)} \nabla \varphi \overrightarrow{ \rm (r) }] = - \frac{1}{\varepsilon_0} \left [ \rho^{fixed} \overrightarrow{ \rm (r) } + e \sum_{i}^{n} C_{i}^{b} exp ( - \frac{ez_i}{kT} \varphi \overrightarrow{ \rm (r) } ) \right ] \end{equation} \end{document}
runs without error and makes this output