\documentclass[12pt]{article}

\usepackage{amsmath}

\begin{document}

\begin{align*}
E = 
\begin{cases}
-\epsilon& \quad r < \sigma \\
-\epsilon\cos\left(\frac{\pi\left(r - \sigma\right)}{2\left(r_c - \sigma\right)}\right)&\quad \sigma \leq r < r_c \\
0& \quad r \geq r_c
\end{cases}
\end{align*}

\end{document}
