Find the net electric force on charge `q` in the following cases , take `(1)/(4 pi in_(0)) (Qq)/(d^(2)) = F_(0)`.
(a)
(e) The point charges `Q , 80 Q , 27 Q ,... , 1000 Q` are placed at `x = d , 2d , 3d , .... , 10 d`. A point charge `q` is placed at origin.

The charges - q, Q, -q are placed along x-axis at x = 0, x = a and x = 2a. If the potential energy of the system is zero, then Q:q is

(a) Two point charges Q and 16 Q are fixed at separation d . Where should a third point charge be placed between them so that it experiences no force I.e. in equilibrium ? (b) In the previous problem , if we replace Q by - Q , where should the third charge be placed on the joining the charges so that it is equilibrium ? (c ) Three point charges Q , q and Q are placed at x = 0 , x = d//2 and x = d . Find q in terms of Q so that all charges are in equilibrium. (d) Two point charges 9 Q and 25 Q are placed at separation d . Where should a third charge q be placed between them so that all charges are in equilibrium ? Also find the value of q and its nature.

A positive point charge q_(1) is placed at (a,0) and another positive point charge q_(2) is placed at (0,a) . Find the force acting on q_(1) .

A positive point charge q_(1) is placed at (a,0) and another positive point charge q_(2) is placed at (0,a) . Find the force acting on q_(1) .

Two fixed point charges + 4q and + q are separated by a distance d. Where should the third point charge be placed for it to be in equilibrium?

(a) The charges each Q are placed at x - d , 2d , 4d ,…oo . Find electric potential at origin O . (b) A charge +Q is placed at each of the points x = d , x = 3d ,x = 5d ,…..,oo on the x -axis , and a charge -Q is placed at each of the points x = 2d , x = 4d , x= 6d , ...,oo .Find the electric potential at the origin O .

(a) The charges each Q are placed at x - d , 2d , 4d ,…oo . Find electric potential at origin O . (b) A charge +Q is placed at each of the points x = d , x = 3d ,x = 5d ,…..,oo on the x -axis , and a charge -Q is placed at each of the points x = 2d , x = 4d , x= 6d , ...,oo .Find the electric potential at the origin O .