Force between multiple charges

Force is among the basic concept of Physics and Science. The concept of force applies everywhere, not only on large scale objects which we see in our day to day life but at molecular level as well which includes, cell, atoms and electric charges as well. 

Just like force, another one such study in physics is electrostatics which means study about electric charge when they are static (No movements). So how these two concepts are interrelated ? Well, as you can see force is a phenomenon which is present everywhere and that’s why even electric charges get affected by force. 

So what’s the problem? Actually we study the force one side only. Here’s what I mean, when we study about force, for example: “Force applied by some object A on another object B” we are only considering a scenario where object A applies force to Object B but reality is not that simple. 

Even though we are finding the force applied by object A on object B but in real world, there are dozens of different objects as well which are applying force on object B and that’s why, the real total force on object B can be only calculated when we consider all the forces acting on it. 

This is the same case with electric charges as well, there are millions of electric charges present in small areas of an object and considering only the force applied by one charge on another is not actually totally true. 

To understand the electrostatics world in better way, we should consider all the forces acting on the charge and this is where the concept of  “Force between multiple charges” comes into play which we are going to understand in this article.   

To formulate this in simpler terms: 

Force acting on electric charge is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between the two charges and the force acting on charge due to multiple charges present around it can be found with the vector sum of of all the individual charges acting on it.

Now, What is vector you may ask ? Lets understand all this in much more detail in this article.  

What is force and Coulomb’s law ?

You can understand force as an interaction between two objects or body which causes the change in state of motion of the body. There is not one definition of force, it’s more like a concept with multiple definitions. The most important thing here is to not know the definition but actually understand the concept and principle. 

Force is the concept in physics which changes the state of motion of an object, it can also be defined as “push” or “pull“. Force is a vector quantity because whenever we apply force, it has some magnitude and is applied in certain direction which makes it a vector quantity. 

You can learn more about vector and scalar quantity in this another article where I have touched this topic of scalar and vector in much more detail. 

In world of electric charge and electrostatics, we find the force between two electric charges using Coulomb’s law which states that force between two charges is directly proportional to the magnitude of the two charges and inversely proportional to the square of distance between them. 

With the help of Coulomb’s law, we can find the formula of force between the two charges using the formula: 

This way, we can find the force between two charges but what about multiple charges ? As we have already discussed, in the real world things are not that simple. So how do we find the actual force acting on the charge. Let’s try to understand this as well. 

Superposition principle:

The Coulomb’s law formula is used to find the force between two charges but in real world there are multiple charges and forces acting from all the different direction on a body and in order to find the total forces on the charge, we need to take all the forces acting on it in consideration with the help of vector. 

Since force is a vector quantity, it has direction as well magnitude and the effect of force will also be different based on the direction, which makes vector a perfect choice to find out the force between multiple charges. 

With the help of vector quantity, we need to find the vector sum of all the forces acting on a body and this is called as superposition theorem.

Let’s take the system of charges with charge Q1, Q2, Q3………Qn where “n” is the total number of charges. In this scenario: 

The total force “FTotal” = F12+F13…….Fn which can also be written like this using coulomb’s formula:

This is the total force acting on a charge due to multiple charges. 


1. Does the sign of charges affect the magnitude of total force due to multiple charges?

No, the sign of charge does not affect the magnitude of the force. The force between the multiple charges of  superposition is consider without any sign, that’s why the magnitude is independent of the sign. 

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