Twelve infinite ling wire of uniform linear charge density ($\lambda$) are passing along the twelve edges of a cube. Find electric flux through any face of cube.
 

 

${\varphi }_{cube}=$ Flux due to single wire from whole cube
${\varphi }_{cube}=\frac{\lambda \mathcal{l}}{8{\epsilon }_0}$ similarly four wires out of twelve will have same contribution and eight will have zero
${\varphi }_{fac{e}_1}=\frac{\lambda \mathcal{l}}{8{\epsilon }_0}\times 4=\frac{\lambda \mathcal{l}}{2{\epsilon }_0}$