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The potential energy of a system of charges equals the work done in assembling them from infinity. For two charges: U = kq1q2/r (positive for like, negative for unlike charges). For N charges, the total PE is the sum over all unique pairs: N(N-1)/2 terms.

For three charges at vertices of a triangle: U = kq1q2/r12 + kq1q3/r13 + kq2q3/r23. For four charges at square corners: 6 terms — 4 side pairs and 2 diagonal pairs with different distances.

The work done to bring a charge q from infinity to a point at potential V is W = qV. If moving between two points: W = q(V_final - V_initial) for work by external agent, or W = q(V_initial - V_final) for work by the field.

Important distinctions: The PE of a charge in an external field (U = qV) is different from the self-energy of a charge distribution (energy to assemble the distribution itself). For a uniformly charged solid sphere: U_self = 3kQ^2/(5R). For a thin shell: U_self = kQ^2/(2R).

An electron accelerated through potential difference V gains kinetic energy eV. The unit eV (electron-volt) = 1.6 x 10^(-19) J is widely used in atomic and nuclear physics.

JEE applications: finding the minimum distance of approach (set KE = PE), escape velocity from charged bodies (set total energy to zero), and binding energy calculations (minimum energy to remove a charge to infinity).