Deduce the expression for the electric filed `oversetto E` due to a system of two charges `q_1 and q_2` with position vectors ` oversetto (r_1) and oversetto (r_2) ` at a point P having position vector ` oversetto ® `.

Explanation

Let as shown two point charges ` q_1 and q_2` be situated at points A and B respectively with positions vectors `oversetto (r_1) and oversetto (r_2) `. Let P be a point having position vector ` oversetto ® `. Electric field at P due to charge `q_1`
` oversetto (E_1) =(1)/(4 pi in _0) .(q_1)/(|oversetto r -oversetto (r_1) |^(3) ) .(oversetto r-oversetto (r_1)) `
and field at P due to charge `q_2 ,oversetto (E_2) =(1)/(4 pi in _0) .(q_2)/(|oversetto r -oversetto (r_2) |) (oversetto r- oversetto (r_1)) `
` therefore ` Total electric field at point P is
` oversetto (E) =oversetto (E_1) +oversetto (E_2) =(1)/(4 pi in _0) [(q_1)/(|oversetto r-oversetto (r_1)|^(3) ).(oversetto r-oversetto(r_1)) +(q_2)/(|oversettor-oversetto(r_2)|) ]`