Redefine \big, \Big, etc. dimension locally

Question

I'd like to redefine \big, \Big etc. commands to change their dimensions for single equations. E.g.

{\makeatletter\renewcommand{\big}{\bBigg@{2}}\makeatother%
\begin{equation}
\big(\frac{1}{2}\big)
\end{equation}}\relax

For practical reasons I'd like to define, in the preamble, a command like this:

\newcommand{\mybig}[1]{\makeatletter\renewcommand{\big}{\bBigg@{#1}}\makeatother}

so to have something like:

{\mybig{2}%
\begin{equation}
\big(\frac{1}{2}\big)
\end{equation}}\relax

But it doesn't work. Where am I wrong?