Electric field due to a number of charges

 

Electric field due to a

number of charges:

Consider a group of charges q_1, q_2, q_3,  q_{4, ..…………..} q_n. are in 

space with position vectors r_1, r_2, r_3, r_{4 …………………..} r_n 

respectively from the origin.

As shown below

Now the electric field intensity at a position S is the electrostatic force experienced by a unit positive charge at S position due to all charges q_1, q_2, q_3,  q_{4, ..…………..} q_n.

So the electric field due to q₁ is

 

Similarly

…………………………………………..

…………………………………………..

So the net electric field intensity is

E = E₁  +   E₂  +  E₃  +  ………….. + E_n 

 

On putting the value of  E₁,  E₂,  E₃, ………….. E_n 

 

We get the following