A uniform electric field of magnitude in air (treat air as vacuum) meets the flat…

PHYSICS · Subjective · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric fields in matter · Maxwell's equations and conservation laws

Electricity, Magnetism and Electromagnetism, Ch Displacement current, Maxwell's equations and boundary conditions

Problem

A uniform electric field of magnitude 800 V m−1800\,\mathrm{V\,m^{-1}} in air (treat air as vacuum) meets the flat surface of a thick slab of polythene of relative permittivity εr=2.3\varepsilon_r = 2.3 at 60∘60^\circ to the normal of the surface. There is no free charge on the surface and the polythene is linear and non-magnetic. A student writes: "Because there is no free charge on the surface, the field crosses it without changing direction, so the field in the polythene is also at 60∘60^\circ to the normal. Its magnitude is reduced by the relative permittivity: E2=800/2.3=348 V m−1E_2 = 800/2.3 = 348\,\mathrm{V\,m^{-1}}." Identify the error in this reasoning and give the correct magnitude of the field in the polythene and the angle it makes with the normal.

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