A flat interface separates region 1

PHYSICS · Multi-part · 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 flat interface separates region 1, which is vacuum, from region 2, a linear dielectric of relative permittivity εr=4.0\varepsilon_r = 4.0. Let n^\hat{\mathbf{n}} be the unit normal pointing from region 1 into region 2. The interface carries a uniform free surface charge density σf=2.0 nC m−2\sigma_f = 2.0\,\mathrm{nC\,m^{-2}}. Just below the surface, in region 1, the electric field has normal component E1⊥=300 V m−1E_{1\perp} = 300\,\mathrm{V\,m^{-1}} along n^\hat{\mathbf{n}}. The fields are static. ((a)) Find the normal component of D\mathbf{D} just above the surface, in region 2. ((b)) Find the normal component of E\mathbf{E} just above the surface, in region 2.

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