Electric Field Due To Plane Sheet of Charge

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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-

 

 

Also Check-

 

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.


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