Minimum potential energy of a point system of charges

For certain values of $N$ we find the distribution of $N$ identical charges on the unit sphere of an $n$-dimensional Euclidean space that minimizes the potential energy $w_n(N)$. For $n\geqslant3$, we find the principal term of the asymptotics of $w_n(N)$ as $N\to\infty$.