A sphere of radius made of a homogeneous

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric fields in matter · Electric fields in matter

Electricity, Magnetism and Electromagnetism, Ch Dielectrics: polarisation, bound charge and the displacement field

Problem

A sphere of radius R=2.0 cmR = 2.0\,\mathrm{cm} made of a homogeneous, isotropic, linear dielectric is uniformly polarised, with P\mathbf{P} of magnitude 4.0×10−6 C m−24.0\times10^{-6}\,\mathrm{C\,m^{-2}} pointing along the +z+z direction. The angle θ\theta is measured from the +z+z axis. The total electric field inside the sphere is uniform, of magnitude 5.0×105 V m−15.0\times10^{5}\,\mathrm{V\,m^{-1}}, and points along P\mathbf{P}. You may use the result quoted in the chapter that the bound charge of a uniformly polarised sphere alone produces a uniform interior field −P/3ε0-\mathbf{P}/3\varepsilon_0. ((a)) Find the bound surface charge density at θ=0\theta = 0, at θ=60∘\theta = 60^\circ and at θ=90∘\theta = 90^\circ. ((b)) Find the magnitude of the field produced inside the sphere by the bound charge alone, and state its direction relative to P\mathbf{P}. ((c)) Find the susceptibility χe\chi_e and the relative permittivity εr\varepsilon_r of the material.

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