Electromagnetism / Electrodynamics I · Fields in matter and polarization
The Lorentz cavity field is not the macroscopic field
Problem
A uniformly polarized cubic dielectric has macroscopic fields $\mathbf E$ and $\mathbf P$. In the Lorentz construction, remove a small spherical region around a molecule while treating all material outside the sphere as a continuum. Show that the continuum contribution to the local field is $\mathbf E_{\rm loc}=\mathbf E+\mathbf P/(3\epsilon_0)$. State what additional contribution has been excluded.
Hint
Represent the removed material by a superposed sphere with opposite polarization.
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