#### 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.

#### Solution

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)`

Is there an error in this question or solution?

Solution 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. Concept: Electric Field - Introduction of Electric Field.