  Let $K$ be a non-polar compact subset of $\mathbb{R}$ and $\mu_K$ denote the
equilibrium measure of $K$. Furthermore, let $P_n\left(\cdot, \mu_K\right)$ be
the $n$-th monic orthogonal polynomial for $\mu_K$. It is shown that
$\|P_n\left(\cdot, \mu_K\right)\|_{L^2(\mu_K)}$, the Hilbert norm of
$P_n\left(\cdot, \mu_K\right)$ in $L^2(\mu_K)$, is bounded below by
$\mathrm{Cap}(K)^n$ for each $n\in\mathbb{N}$. A sufficient condition is given
for
$\displaystyle\left(\|P_n\left(\cdot;\mu_K\right)\|_{L^2(\mu_K)}/\mathrm{Cap}(K)^n\right)_{n=1}^\infty$
to be unbounded. More detailed results are presented for sets which are union
of finitely many intervals.
