# Electric Field Due To Plane Sheet of Charge

## 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/εo 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,

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-

1. Left end cap
2. Right end cap
3. 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-

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