  We give an application of our earlier results concerning the quasiconformal
extension of a germ of a conformal map to establish that in two dimensions the
equipotential level lines of a capacitor are quasicircles whose distortion
depends only on the capacity and the level. As an application we find that
given disjoint, nonseparating and nontrivial continua $E$ and $F$ in
$\hat{\mathbb{C} }=\mathbb{C} \cup\{\infty\}$, the closed hyperbolic geodesic
generating the fundamental group $\pi_1\big(\hat{\mathbb{C} }\setminus (E\cup
F) \big) \cong \hat{\mathbb{Z} }$ is a $K$-quasicircle separating $E$ and $F$
with explicit distortion bound depending only on the capacity of
$\hat{\mathbb{C} }\setminus (E\cup F)$. This result is then extended to obtain
distortion bounds on a quasicircle representing a given homotopy class of a
simple closed curve in a planar domain. Finally we are able to use these
results to show that a simple closed hyperbolic geodesic in a planar domain is
a quasicircle with a distortion bound depending explicitly, and only, on its
length.
