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In a series of papers, Kempf and co-workers (J. Phys. A: Math. Gen. {\bf 30},2093, (1997); Phys. Rev. D {\bf52}, 1108, (1995); Phys. Rev. D {\bf55}, 7909,(1997)) introduced a D-dimensional $(\beta,\beta')$-two-parameter deformedHeisenberg algebra which leads to a nonzero minimal observable length. In thiswork, the Lagrangian formulation of an electrostatic field in three spatialdimensions described by Kempf algebra is studied in the case where$\beta'=2\beta$ up to first order over deformation parameter $\beta$. It isshown that there is a similarity between electrostatics in the presence of aminimal length (modified electrostatics) and higher derivative Podolsky'selectrostatics. The important property of this modified electrostatics is thatthe classical self-energy of a point charge becomes a finite value. Twodifferent upper bounds on the isotropic minimal length of this modifiedelectrostatics are estimated. The first upper bound will be found by treatingthe modified electrostatics as a classical electromagnetic system, while thesecond one will be estimated by considering the modified electrostatics as aquantum field theoretic model. It should be noted that the quantum upper boundon the isotropic minimal length in this paper is near to the electroweak lengthscale $(\ell_{electroweak}\sim 10^{-18}\, m)$.

Formulation of an Electrostatic Field with a Charge Density in the Presence of a Minimal Length Based on the Kempf Algebra