A dielectric sphere of radius sits in a uniform applied field .

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

The Boundary-Value Problem, Ch Linear dielectrics and the boundary-value problem with matter in it

Problem

A dielectric sphere of radius a=1.5 cma = 1.5\,\mathrm{cm} sits in a uniform applied field E0=2.0×104 V m−1E_0 = 2.0\times10^{4}\,\mathrm{V\,m^{-1}}. ((a)) For εr=1,4,10,80\varepsilon_r = 1, 4, 10, 80, compute the uniform interior field Ein=3εr+2E0E_{\rm in} = \dfrac{3}{\varepsilon_r+2}E_0. ((b)) For the same four values of εr\varepsilon_r, compute the induced dipole moment p=4πε0a3εr−1εr+2E0p = 4\pi\varepsilon_0a^3\dfrac{\varepsilon_r-1}{\varepsilon_r+2}E_0. ((c)) State in one sentence whether EinE_{\rm in} ever reaches zero for any finite εr\varepsilon_r, and what this says about treating a dielectric sphere as if it excluded the field like a conductor.

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