Three electric point charges `q_(0) , q_(1)` and `q_(2)` are at distance `r_(0) , r_(1)` and `r_(2)` , respectively with respect to same origin . What is the force on charge `q_(0)` in the field of charges `q_(1)` and `q_(2)` ?

Explanation

Force on `q_(0)` due to `q_(1)` is
`F_(1) = (k q_(1) q_(0))/(|r_(0) - r_(1)|^(2)) xx (r_(0) - r_(1))/(|r_(0) - r_(1)|) = (k q_(1) q_0)/(|r_(0) - r_(1)|^(3)) xx (r_(0) - r_(1))`
Similarly force on `q_(0)` due to `q_(2)` is `F_(2) = (k q_(2) q_(0))/(|r_(0) - r_(2)|^(3)) xx (r_(0) - r_(2))`
Resultant force on `q_(0)` is `R = F_(1) + F_(2) = (k q_(1) q_(0))/(|r_(0) - r_(1)|^(3)) xx (r_(0) - r_(1)) + (k q_(2) q_(0))/(|r_(0) - r_(2)|^(3)) xx (r_(0) - r_(2))`