The derivation of Laplace’s and Poisson’s equations assumed constant permittivity, but the...

The derivation of Laplace’s and Poisson’s equations assumed constant permittivity, but there are cases of spatially varying permittivity in which the equations will still apply. Consider the vector identity, ∇ · (ψG) = G · ∇ ψ + ψ ∇ · G, where ψ and Gare scalar and vector functions, respectively.

Figure 6.14 See Problem 6.39.

Determine a general rule on the allowed directions in which ϵ may vary with respect to the local electric field.