Abstract: We derived a simplified formula of electrostatic energy for the two unlike spheres at constant surface potential using the rotation method, recently developed to calculate electrostatic energy of any shape particles. Surface integral of the mean curvature M_0=4π·2a_1a_2/(a_1+a_2), interaction energy of the supporting planes
V=εκ/4·{(ψ_1+ψ_2)~2(1-thκρ/2) - (ψ_1-ψ_2)~2(cthκρ/2-1)},
which is derived by HHF, where ε =delectric constant, κ =Debye-Hckel parameter, ψ_1 and ψ_2 =surface potential, ρ =shortest distance between dissimilar plates. Substituting M_0 and V into V_(WJZ)=∫Vd(s-2πρ~2), We obain
V_(WJZ)=(επa_1a_2)/(a_1+a_2){(ψ_1+ψ_2)~2ln[1+exp(-κρ)]×[1-(κρ+α_1)/(2β_1) (1/(κa_1)+1/(κa_2)]+(ψ_1-ψ_2)~2ln[1-exp(-κρ)]·[1-(κρ+α_2)/(2β_2)×(1/(κa_1)+1/(κa_2)]}
Numerical values of V_(WJZ) are compared with those of OCHW and BM, it approaches results of OCHW, However, when a_1/a_2>10 error of the rotation method increases.