The change in some thermodynamic quantities such as Gibbs' free energy, entropy and enthalpy of the binding of two DNA strands (forming a double helix), while one is tethered to a surface and are analytically calculated. These particles are submerged in an electrolytic solution; the ionic strength of the media allows the linearized version of the Poisson-Boltzmann equation (from the theory of the double layer interaction) to properly describe the interactions . There is experimental and computational evidence that an ion penetrable ellipsoid is an adequate model for the single strand and the double helix [22-25]. The analytic solution provides simple calculations useful for DNA chip design. The predicted electrostatic effects suggest the feasibility of electronic control and detection of DNA hybridization in the fast growing area of DNA recognition.