1.7 Coulomb's Force due to a Number of Point Charges (Super position Principle)

Electric force between two charges is given by Coulomb's law. Let us calculate the force on a charge due to several point charges in it's neighborhood.
       Consider a system of three charges q1,q2 and q3. Let r1,r2, and r3 be the position vectors of these charges from an arbitrary origin O.
          Force is a vector quantity. Hence vector law of addition can be used to find the resultant force acting on the charge q1.


        Force on q1 due to q2 is Vector F12
Simillarly,
        Force on q1 due to q3 is Vector F13

Therefore resultant force on charge q1 is
       vector F1 = vector F12 + vector F13
   
                   If we consider a system of charges q1, q2,.....qn What is the resultant force on q1 due to q2,q3,.........qn?

 Using vector law of addition , vector F1 is the summation of vector F12,F13,......F1n

 The force on one charge say q1, due ot other charges can be obtained by performing a vector addition of the forces due to other charges. This method of addition of forces is termed as principle of super position in electrostatics.
     Super position principle can be stated like this  , The force on a point charge due to  a number of point charges is equal to the vector sum of forces due to individual charges.