Figure shows three charges `q_1 , q_2` and `q_3` . What forces acts on `q_1` , if `q_(1) = 1 mu C , q_(2) = 3 mu C ` and `q_(3) = - 2mu C , r_(12) = 0.15 m , r_(13) = 0.1 m , theta = 30^(@)` ?

Explanation

The force due to charges `q_(3)` and `q_2` on `q_1` is shown in the figure given below by forces `F_(3)` and `F_(2)` , respectively .

Resolving into horizontal and vertical axis as shown in the figure given below .

The net force in vertical axis is `|F_(y)| = F_(3) cos theta`
`= ((1)/(4 pi epsi_(0)) xx (q_(3) q_(1))/((r_(13))^(2))) cos 30^(@)`
`=[ (9 xx 10^(9) xx 2 xx 10^(-6) xx 1 xx 10^(-6)])/((0.1)^(2)) ] 0.866`
`|F_(X)| = 1.56 N`
The net force in horizontal axis is `|F_(X)| = (F_(2) + F_(3) sin theta)`
`= [ ((1)/(4 pi epsi_(0)) (q_(1) q_(2))/(r_(12)^(2))) + ((1)/(4pi epsi_(0)) (q_(1) q_(3))/(r_(13)^(2))) sin theta]`
`((9 xx 10^(9) xx 1 xx 10^(-6) xx 3 xx 10^(-6))/((0.15)^(2))) + (( 9 xx 10^(9) xx 1 xx 10^(-6) xx 2 xx 10^(-6))/((0.1)^(2))) sin 30^(@)`
`|F_(X)| = 1.2 + 0.9 = 2.1` N
`therefore` Net force of both charges on charges `q_(1)` is `= sqrt((F_X)^(2) + (F_(y))^(2))`
`= sqrt(1.56)^(2) + (2.1)^(2)) = 2.62` N