**Gauss’s Law-**

Before you go through this article, make sure that you have gone through the previous article on **Gauss’s Law**.

**We have learnt-**

- Gauss’s Law helps to find the total electric flux through any closed surface.
- It states that the total electric flux through any closed surface is 1/ε
_{o}times the net charge enclosed within it.

**Applications of Gauss’s Law-**

Using Gauss’s law, we can easily calculate the electric field due to a-

- thin infinite long line charge
- thin infinite plane sheet of charge
- uniformly charged thin spherical shell

**In this article, we will discuss the electric field due to a thin infinite plane sheet of charge.**

**Electric Field Due To A Thin Infinite Plane Sheet Of Charge-**

Consider a thin infinite plane sheet having a uniform surface charge density σ Cm^{-2 }as shown-

**Direction of Electric Field-**

**By symmetry, the electric field due to a plane sheet of charge is directed-**

- perpendicularly outwards if the sheet carries a positive charge
- perpendicularly inwards if the sheet carries a negative charge

**Magnitude of Electric Field-**

To calculate the magnitude of electric field intensity E at a point P located at a distance r from the sheet using Gauss’s law, **we consider an imaginary closed cylinder of length r on each side of the sheet with end caps of area A as the Gaussian surface**.

**A cylinderical Gaussian surface is an ideal choice because-**

**At every point on the curved surface of cylinder,**

- the angle between
**electric field intensity**and area element is 90°. - So, the
**electric flux**passing through it will be zero.

**At every point on the end caps of cylinder,**

- the magnitude of electric field intensity is constant.
- the angle between
**electric field intensity**and area element is 0°.

**According to Gauss’s theorem, we have-**

**(Equation-01)**

The cylinderical Gaussian surface can be divided into three parts-

- Left end cap
- Right end cap
- Curved surface

**Then, equation-01 can be written as-**

**Graph-**

**Clearly, the electric field intensity due to a thin infinite plane sheet of charge is independent of the distance of observation point from the sheet i.e.**

**The graph showing the variation of electric field intensity due to a thin infinite plane sheet of charge with distance from it is-**

**Also Check-**

**Electric field due to a thin Infinite long line charge****Electric field due to a charged thin spherical shell**

**Read the next article on-**

**Electric Field Due To Charged Thin Spherical Shell**

**Get more notes & other study material of the Chapter** **Electric Charges & Field**.