# Scaling of nuclear and electromagnetic force

The Wikipedia article on alpha decay stated:

The strength of the attractive nuclear force keeping a nucleus together is thus proportional to the number of nucleons, but the total disruptive electromagnetic force trying to break the nucleus apart is roughly proportional to the square of its atomic number.

How can this linear/quadratic scaling be justified? To me it is anything but obvious.

The electromagnetic repulsion between protons is much weaker than the nuclear attraction at short ($$\sim 1$$ fm) ranges, but it falls off much more slowly with distance than the (exponentially decaying) strong interaction. So there is a substantial positive potential between every single pair of protons in a nucleus. For atomic number $$A$$, the number of pairs is $$A(A-1)/2$$, so the total (positive) electromagnetic potential energy scales like $$A^{2}$$.