  A modified version of the Reissner-Nordstrom metric is proposed on the
grounds of the nonlinear electrodynamics model. The source of curvature is an
anisotropic fluid with $p_{r} = -\rho$ which resembles the Maxwell stress
tensor at $r >> q^{2}/2m$, where $q$ and $m$ are the mass and charge of the
particle, respectively. We found the black hole horizon entropy obeys the
relation $S = |W|/2T = A_{H}/4$, with $W$ the Komar energy and $A_{H}$ the
horizon area. The electric field around the source depends not only on its
charge but also on its mass. The corresponding electrostatic potential
$\Phi(r)$ is finite everywhere, vanishes at the origin and at $r = q^{2}/6m$
and is nonzero asymptotically, with $\Phi_{\infty} = 3m/2q$.
