Question

how does the electric field due to a plane sheet of charge change when the distance of point is increased​

Answer 1

Electrostatic Field Intensity due to infinite sheet of charge is independent of the distance from the sheet.

Proof:

Let us consider an infinite sheet of positive charge from which electric field lines shall emerge on either sides.

We will consider a cylindrical Gaussian Surface on either side of the sheet.

Let cross-sectional area of Cylinder be A and the Electrostatic Field Intensity be E;

Electric Flux comes out of the Gaussian Surface from both sides, hence total flux will be equal to 2EA .

Considering Gauss' Law ;

$\therefore \displaystyle \: \int \: E \: ds = \dfrac{q}{ \epsilon_{0}}$

$= > 2 \times (EA) = \dfrac{q}{ \epsilon_{0}}$

Expressing charge in terms of surface-charge-density :

$= > 2 \times (EA) = \dfrac{ (\sigma \times A)}{ \epsilon_{0}}$

$= > E= \dfrac{ \sigma }{ 2\epsilon_{0}}$

Hence Electrostatic Field Intensity doesn't change with distance from sheet .