\documentclass[preview]{standalone}
\usepackage{varwidth}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath,amssymb,amsthm,bm}
\begin{document}
\begin{varwidth}{50in}
  \begin{equation}
    \bm{H}_{ex} ~=~ -\sum_{i,j,i\neq j}^{N} {J} \left(r_{ij} \right)\, \vec{s}_{i}\cdot \vec{s}_{j} \nonumber
  \end{equation}
\end{varwidth}
\end{document}
