forces between multiple charges

 

Principle of superposition:

forces between multiple charges

 

In a system where more than two point charges are there, coulomb’s law do not perform well. In that scenario the net electrostatic force acting on any charged particle due to a number of other charged particles is equal to the vector sum of all forces acting on that particle on a particular moment.

 

The individual forces are unaffected by the presence of other charged particle. This is called the principle of superposition.

 

 

Suppose q₀ is the charge & we have to calculate the electrostatic force acting on it. r₀  is the position vector of q_0.

 

 

Suppose other charges are q_1, q_2, q_3,  q_{4, ..…………..} q_n. Again

r_1, r_2, r_3, r_{4 …………………..} r_n are the position vectors of

q_1, q_2, q_3,  q_{4, ..…………..} q_n respectively.

 

 

Now according to superposition of electrostatic forces, the net force acting on the charge q₀ is

Where

 

Now from the vector form of Coulomb’s law is

 

Or

Similarly

Therefore from (1)