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?
Let the charge at point 2q be placed at point P as shown. The force due to q is to the left and that due to −3q is to the right.
∴2q24πϵ0x2=6q24πϵ0(d+x)2⇒(d+x)2=3x2
∴2x2−2dx−d2=0⇒x=d2±√3d2
(−ve sign would be between q and −3q and hence is unacceptable.)
⇒x=d2+√3d2=d2(1+√3) to the left of q.