Atlearner-
April 19, 2023

April 13, 2022

We know that two like or similar charges repel each other and two opposite charges attract each other. *Coulomb's law* reveals these forces that are working in the charges ( To know the details of Coulomb's law click here... ).

But force is a vector quantity, so it has both magnitude and direction. That is why Coulomb's law can be re-written in the form of vectors.

Consider in a Cartesian coordinate system there are two similar point charges *q**1* and *q**2* are in positions A and B respectively. Here *r**1* is the position vector of points A and *r**2* is the position vector of point B relative to the origin *O* of the system.

We will determine - 1. *The force that is acting on the charge q1 due to the chare q2* and 2. *The force that is acting on the charge q2 due to the charge q1*.

1. The force that is acting on the charge *q**1* due to the chare *q**2* :

This is the vector form of Coulomb's Law.

We can also write this vector form of coulomb's law in terms of unit vector notation

2. The force that is acting on the charge *q**2* due to the charge *q**1* :

We can also write this vector form of coulomb's law in terms of unit vector notation

This says that the forces that are working in the electrical charge particle are equal but opposite, which is Newton's third law of motion. Thus, Coulomb’s law agrees with Newton’s third law.

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