In classical electrostatics, we learn that the electrostatic potential of an electric dipole at a distance $r$ is proportional to $1/r^2$. Then putting two dipoles together to form a quadrupole, the potential goes as $1/r^3$ and so on.

Does this mean that the electrostatic potential energy gets smaller the more "poles" the system has? And if so, isn't this counter-intuitive since it would take more work (and defining electrostatic energy as the amount of work needed to move electric charges, according to Griffiths's Introduction to Electrodynamics) to assemble a system containing more charges - hence a system containing more charges should have more electrostatic potential energy?


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