**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 an infinite line charge.**

**Electric Field Due To A Thin Infinitely Long Line Charge-**

Consider a thin infinitely long straight wire having a uniform linear charge density λ Cm^{-1} as shown-

**Direction of Electric Field-**

**By symmetry, the electric field due to a line charge is directed-**

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

**Magnitude of Electric Field-**

By symmetry, the magnitude of electric field intensity is same at all points equidistant from the line charge.

To calculate the magnitude of electric field intensity E at a point P located at a distance r from the line charge using Gauss’s law, **we consider an imaginary cylinder of radius r as the Gaussian surface**.

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

- At every point on the curved surface of cylinder, the magnitude of
**electric field intensity**is constant. - The
**electric flux**passing through the circular faces of cylinder will be zero.

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

**(Equation-01)**

The cylinderical Gaussian surface can be divided into three parts-

- Top circular face
- Bottom circular face
- Curved surface

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

**In terms of Coulomb’s Constant, the above expression for electric field intensity can be rewritten as-**

**Graph-**

**Clearly, the electric field intensity due to an infinite line charge is inversely proportional to the distance of observation point from the line charge i.e.**

**The graph showing the variation of electric field intensity due to an infinite line charge with distance from it is-**

**Also Check-**

**Electric field due to a thin infinite plane sheet of charge****Electric field due to a charged thin spherical shell**

**Read the next article on-**

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

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