An infinite plane slab of electret is uniformly polarised with

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

The Boundary-Value Problem, Ch Polarisation and bound charge, completed

Problem

An infinite plane slab of electret is uniformly polarised with P=Pz^\mathbf{P} = P\hat{\mathbf{z}}, perpendicular to its two flat faces, where P=2.0×10−6 C m−2P = 2.0\times10^{-6}\,\mathrm{C\,m^{-2}}. The slab carries no free charge anywhere, and it is isolated (no external applied field). Edge effects are ignored (the slab is treated as infinite in extent). ((a)) Find the bound surface charge density on the top face (outward normal +z^+\hat{\mathbf{z}}) and on the bottom face (outward normal −z^-\hat{\mathbf{z}}). ((b)) Using the depolarising factor appropriate to this shape and orientation, find the uniform macroscopic field E\mathbf{E} inside the slab. ((c)) A narrow needle-shaped hole is drilled through the slab along z^\hat{\mathbf{z}} (along P\mathbf{P}). Find the field a probe would read inside this needle cavity.

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