Physics

Problem

Identify the correct expression for the electrostatic potential energy

U

between two nuclei of charges

Z_1e

and

Z_2e

separated by a distance

r

in vacuum. a)

U = \dfrac{1}{4\pi\varepsilon_0}\dfrac{(Z_1+Z_2) e^2}{r}

U = -\,\dfrac{1}{4\pi\varepsilon_0}\dfrac{Z_1 Z_2 e^2}{r}

U = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Z_1 Z_2 e^2}{r}

U = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Z_1 Z_2 e^2}{2r}

Intuitive explanation

The electrostatic potential energy between two point charges is fundamentally about how much work you'd need to do to assemble them from infinity. Use Coulomb's law as your starting point—the force between the nuclei—then integrate to find the energy stored in their configuration. The key insight is that potential energy depends on the product of the charges and inversely on separation, with Coulomb's constant $k$ setting the scale.

Intuitive explanation

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