energy density as a function of position on the $Q{\bar Q}$ axis, $\x = x\hat{\R}$, for $R=|\R|=10\mbox{ fm}$. The small oscillations come from the sharp-cutoff introduced by the $\theta$-functions in [Eq. (\[f\])]{} which produces the Bessel’s functions in [Eq. (\[elnof\])]{}. For a smooth cutoff, [*e.g.*]{} with $\theta(\mu - p) \to \exp(-p/\mu)$ in [Eq. (\[elnof\])]{} one should replace $1 - j_0(\mu|\R/2-\x|)$ by $1 - \arctan(\mu|\R/2-\x|)/\mu|\R/2-\x|$. The cut-off is also responsible for the rapid variations near the quark positions, $\x = \pm R/2$.

We note that for large separations between the quarks, $R >> 1/\mu$ and $x << R$, the Coulomb energy density behaves as expected from dimensional analysis, $$\langle \E^2(\x,R\mu\to \infty) \rangle \to {{32 b_C}\over {\pi^3R^2}}.
 \label{short}$$ which is consistent with linear confinement, [*i.e.*]{} if $\langle \E^2(\x,R\mu\to \infty) \rangle$ is integrated over $\x$ in the region $|\x|<R$ on obtains $V_C(R)  \propto R$.

At large distances $x >> R >> 1/\mu$ we obtain $$\langle \E^2(|\x|/R \to \infty,R\mu\to \infty) \rangle \to 
 {{2 b_C R^2}\over {\pi^3\x^4}}. \label{inf}$$ If there were a finite correlation length one would expect $\langle \E^2(|\x|/R \to \infty,R\mu\to \infty)\rangle$ to fall-off exponentially with $|\x|$ [@DDS] and not as a power-law. The power-law behavior obtained in Eq. (\[inf\]) is again related to 