If a system contains four particles, how many potential energy pairs U₁₂, etc., are there? List them.

The negative work done by internal forces on the particles in a system equals the potential energy of the system. It has something to do with particle separation in general.

The longer the distance between two points, the higher the potential energy. The less separation there is, the less potential energy there is.

The sum of the interaction energies of all pairs of particles in the system, the potential energy, is the force exerted on each particle by each other particle in the system:

So, if system have four particles, each one will have an effect on the other three, and the pairs will be as follows

(U₁₂ , U₁₃ , U₁₄ , U₂₃ , U₂₄ , U₃₄ )

Hence, system has six potential energy pairs (U₁₂ , U₁₃ , U₁₄ , U₂₃ , U₂₄ , U₃₄ ).