Conservation laws, implied by the fundamental plasma fluid equations describing the E¿B gradient drift instability in ionospheric plasma clouds, are utilized to obtain an analytic prescription for the power spectrum. Furthermore, it is shown that the two-dimensional power law power spectra of magnetic field line integrated Pedersen conductivity (density) perturbations, in the plane perpendicular to the ambient magnetic field, computed from numerical simulation studies and experimental results are supported by an analysis of these conservation laws. The numerical simulations suggest a two-dimensional power spectrum of the form P(k,ϑ) = P0cosmϑ(1+(k/k0)2)-(n+1)/2, where cos ϑ = k⋅E0 and E0 is the ambient electric field. The present analytic formulation suggests 1<n<3. In addition, if m = 2 and n = 2, one finds the outer scale wave number k0∝L-1, the plasma cloud gradient scale length.