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/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-

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-

 

 

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.