Find the field inside a sphere of linear dielectric material in an otherwise uniform electric field E₀ (Ex. 4.7) by the following method of successive approximations: First pretend the field inside is just E 0, and use Eq. 4.30 to write down the resulting polarization P₀. This polarization generates a field of its own, E₁ (Ex. 4.2), which in turn modifies the polarization by an amount P₁, which further changes the field by an amount E₂, and so on. The resulting field is E₀ + E₁ + E₂ + .. Sum the series, and compare your answer with Eq. 4.49.