(a) Three point charges q,-4q and 2q are placed at the vertices of an equilateral triangle ABC of side 'l' as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge q.
(b) Find out the amount of the work 4one to separate the charges at infinite distance.

Explanation

(a) `F_(1) = (k 2q^(2))/(l^(2))`
`F_(2) = (4q^(2))/(l^(2))`
`F_("net") = sqrt(F_(1)^(2) + F_(2)^(2) + 2F_(1)F_(2) cos 120^(@))`
`F_("net") = sqrt(F_(1)^(2) - F_(2)^(2) - F_(1)F_(2))`
(b) Work done required to separate the charge at infinity equal to electric potential energy of system.
`w_(1) = (kq2q)/(l) " "w_(2) =(k(-4q)-q)/(l)`
`w_(3) = (k(-4q) (2q))/(l) " "w = w_(1) + w_(2) + w_(3)`
`w= (2kq^(2))/(l) - (4kq^(2))/(l) -(8kq^(2))/(l) " "w = (-10 kq^(2))/(l)`