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

Two free point charges each of +4q and +q are placed at a distance a apart. Where should a third point charge Q be placed between them so that the entire system is in equilibrium?

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 point charges +9e and +e are kept 16 cm . Apart from each other. Where should a third charge q be placed between them so that the system is in equlibrium state:

Two point charges +9e and +e are kept 16 cm . Apart from each other. Where should a third charge q be placed between them so that the system is in equlibrium state:

(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 fixed point charge 4Q and 2Q are separated by a distance x. where should a third point charge q be placed for ti to be in equilibrium?

Two point charges +q and -q are placed d distance apart. What is the zero potential plane for them?

Two point charges +9e and +e are kept 16 cm . Apart from each other. Where should a third charge q be placed between them so that the system is in equilibrium state:

Two point charges +q and -q are placed a distance x apart. A third charge is so placed that at the three charges are in equilibrium. Then