Apoint charge +2q is at the origin and a point charge −q is located along the x axis at x = d as in the figure below. find a symbolic expression for the net force on a third point charge +q located along the y axis at y = d. (use the following as necessary: ke, the coulomb constant, q, and d.)

Force F1, exerted by the charge +2Q located at the origin over the charge +Q at y =d

F1 =  [ k (+2Q) * (+Q) / (d^2) ] j =  [2KQ^2 / d^2] j

Force F2, exerted by the charge -Q located at x = d over the charge + Q located at y = d

Horizontally: F2,x = [k (-Q)(+Q) / (2d^2) ] cos(45°) i = - [KQ^2 / 2d^2] (√2) / 2 i

=- [KQ^2 (√2) / 4d^2]  i

Vertically: F2,y =  [k (-Q)(+Q) / (2d^2) ] sin(45°) j = - [KQ^2 / 2d^2] (√2) / 2 j =

= - [KQ^2 (√2) / 4d^2]  j

Now sum the respective components

Net force = - [KQ^2 (√2) / 4d^2]  i +  [2KQ^2 / d^2] j - [KQ^2 (√2) / 4d^2]  j

Net force = - [KQ^2 (√2) / 4d^2]  i +  [KQ^2 / d^2](2 - (√2)/4 ) j

- [KQ^2 (√2) / 4d^2]  i +  [KQ^2 / d^2](2 - (√2)/4 ) j