Q.Four systems of charges, each involving charges of magnitude $Q$, $-Q$ or $-2Q$ separated by distances $r$ or $2r$ as shown in the figure, are labelled 1, 2, 3 and 4. Rank the electrostatic potential energies of the four systems in increasing order.

The electrostatic potential energy of a system of point charges is defined as the total work required to assemble that configuration, bringing each charge in, one at a time, from an initial separation of infinity, against the combined field of whichever charges are already in place. For just two charges, this gives U = k q1 q2/r12: positive for two like charges (work must be done against their mutual repulsion to bring them together) and negative for two unlike charges (the field itself does positive work pulling them together). For three or more charges, the same procedure -- bringing each new charge in against the field of all previously placed charges -- gives a sum over every distinct pair, U = k[q1q2/r12 + q1q3/r13 + q2q3/r23 + ...], one term for every p …