$ \begin{equation*} \left.\begin{aligned} \nabla\cdot \bar{B}&=0\\ \oint_S \bar{B}\cdot d\bar{S}&=0 \end{aligned}\right\} \longrightarrow \Phi=\oint_S \bar{B}\cdot d\bar{S} \Longrightarrow \boxed{ \Phi=\oint_S \bar{B}\cdot d\bar{S}=0} \end{equation*} $
The magnetic flux through this closed surface is $ \Phi $
$ \begin{equation*} \boxed{\Phi=0} \end{equation*} $
