Let the position vectors of charges *q*_{1} and *q*_{2} are **r**_{1} and **r**_{2} respectively **Fig.** We denote force on *q*_{1} due to *q*_{2} by **F**12 and force on *q*_{2} due to *q*_{1} by **F**21. The two-point charges *q*_{1} and *q*_{2} have been numbered 1 and 2 for convenience and the vector leading from 1 to 2 is denoted by **r**_{21}:

**r**_{21} = **r**_{2} – **r**_{1}. In the same way, the vector leading from 2 to 1 is denoted by **r**_{12}: **r**_{12} = **r**_{1} – **r**_{2} = – **r**_{21} .The magnitude of the vectors **r**_{21} and **r**_{12} is denoted by *r*_{21} and *r*_{12}, respectively (*r*_{12} = *r*_{21}). The direction of a vector is specified by a unit vector along the vector. To denote the direction from 1 to 2 (or from 2 to 1), we define the unit vectors:

Coulomb’s force law between two point charges *q*_{1} and *q*_{2} located at **r**_{1} and **r**_{2} is then expressed as

If *q*_{1} and *q*_{2} are of the same sign (either both positive and both negative), **F**_{21} is along ˆ**r** _{21}, which denotes repulsion, as it should be for like charges. If *q*_{1} and *q*_{2} are of opposite signs, **F**21 is along – ˆ**r **_{21}(= ˆ**r **_{12}), which denotes attraction, as expected for unlike charges.

Thus, we do not have to write separate equations for the cases of like and unlike charges. The force **F**12 on charge *q*_{1 }due to charge *q*_{2}, is obtained from force **F**21, by simply interchanging 1 and 2, i.e.

**Thus, Coulomb’s law agrees with Newton’s third law.**

### Few Questions Related to Coulombs Law:

**Q1:** When a plastic comb is passed through dry hair, what type of charge is acquire by comb?

**Q2:** Does motion of a body affect its charge?

**Q3: **What is the origin of frictional forces?