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

Given:
Total charge on the rod = Q

The length of the rod = edge of the hypothetical cube = l
Portion of the rod lying inside the cube, `"x" ="l"/2`

Linear charge density for the rod = `"Q"/"l"`

Using Gauss's theorem, flux through the hypothetical cube,

Ø = (Q_in/∈₀) , where Q_in = charge enclosed inside the cube
Here, charge per unit length of the rod = `"Q"/"l"`

Charge enclosed,  `Q_("in") = "Q"/"l" xx "l"/2 = "Q"/2`

Therefore , Ø = ` ("Q"/2)/∈_0 = "Q"/(2∈_0)`