Question

A positively charged rod having uniform linear charge density lambda C/m all over it, is placed in 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:

A positively charged rod having uniform linear charge density lambda C/m all over it, is placed in a hypothetical cube of edge l with the centre of the cube at one end of the rod.

To find:

Minimum possible flux ?

Calculation:

Minimum electric flux is possible only when the enclosed charge within the cube is minimum. That in turn is possible when the rod is placed parallel to the side passing perpendicular to one face.

• Refer to diagram for clear understanding.

$\rm \therefore \: q_{enclosed} = length \times linear \: density$

$\rm \implies \: q_{enclosed} = \dfrac{l}{2} \times \lambda$

$\rm \implies \: q_{enclosed} = \dfrac{l}{2} \times C$

$\rm \implies \: q_{enclosed} = \dfrac{Cl}{2}$

Now, apply GAUSS' LAW:

$\rm\therefore \: \phi = \dfrac{ q_{enclosed}}{ \epsilon_{0}}$

$\rm \implies \: \phi = \dfrac{Cl}{2 \epsilon_{0}}$

So, minimum flux possible:

$\boxed{ \bf \: \phi = \dfrac{Cl}{2 \epsilon_{0}} }$