Question

A charge Q is uniformly distributed over a rod of length `l`. Consider a hypothetical cube of edge `l` with the centre of the cube at one end of the rod. Find the minimum possible flux of the electric field through the entire surface of the cube.

Answer 1

According to Gauss law : Flux depends upon charge inside the closed hypothetical surface. So for minimum possible flux through the entire surface of the cube, charge inside it should be minimum.
Linear charge density of rod `=Q/l`
and minimum length of rod inside the cube `=l/2`
So, charge inside the cube `=l/2 . Q/l=Q/2`
So, fluc through the entire surface of the cube `=(Sigmaq)/in_(0)=Q/(2 in_(0))`