# 3 point charges lie along a straight line with positive charge at the centre and negetive at the ends all are ‘a’ distance apart from each other.The energy needed to exchange the position of the central positive charge with one of the negetive charge is...............???

Raman Mishra
67 Points
5 years ago
Let the charges be -q, +q and -q.
Distance between two charges = a
Energy of the system $U =\frac{ 1q_{i}q_{j}}{4\pi \varepsilon r_{ij}} ; i=1,2,3; j=1,2,3 ;i\neq j$
putting the values we get Uinitial = $-\frac{3q^{2}}{8\pi \varepsilon a}$
Final energy of the system, Ufinal = $-\frac{q^{2}}{8\pi \varepsilon a}$
Therefore, work required = Ufinal -  Ufinal
= $-\frac{q^{2}}{4\pi \varepsilon a}$
However, the system will become unstable and eventually collapse.