**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.

**In this article, we will deduce Coulomb’s Law from Gauss’s Law.**

**Coulomb’s Law From Gauss’s Law-**

**Coulomb’s law** and Gauss’s law are complementary to each other i.e. any of the two can be regarded as basic and then the other can be derived out of it.

**To derive Coulomb’s law from Gauss’s law, consider two point charges Q _{1} and Q_{2} separated by a distance r as shown-**

We draw a spherical Gaussian surface of radius r with O as the center and calculate the **electric field intensity** on it using Gauss’s law.

**According to Gauss’s theorem,**

**Clearly,**

- The angle between electric field intensity and elemental area vector over the surface at any point = 0°
- The charge enclosed by the Gaussian surface, q
_{enc}= Q_{1}

**Substituting and solving, we have-**

**This is the value of electric field intensity at the position of charge Q _{2}.**

**Therefore, force experienced by charge Q _{2} is given by-**

**This is a mathematical form of Coulomb’s law.**

**Hence, Coulomb’s law is derived from Gauss’s law.**

**Read the next article on-**

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