Two point metal charges`-q` and `+2q` are placed at a certain distance apart.Where should a third point charge be placed so that it is in equilibrium?

Two fixed charges are as shown. Where should the third charge be placed so that its in equilibrium?

Two points charges +4 and +q are separated by distance r, where should a third point charge Q be placed that the whole system remains in equilibrium

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

Two point charges 2q and 8q are placed at a distance r apart. Where should a third charge -q be placed between them so that the electrical potential energy of the system is a minimum

(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.

Two point charges +4q and +q are placed at a distance L apart. A third charge Q is so placed that all the three charges are in equilibrium. Then location. And magnitude of the third charge will be

Two charges q and 3q are placed fixed on x-axis separated by distance 'd'. Where should a third charge 2q be placed such that it will not experience any force ?