At a point inside a solid whose polarisation is frozen in
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
At a point inside a solid whose polarisation is frozen in, the macroscopic field is E=2.0×104Vm−1 and the polarisation there is P=6ε0E, with E and P parallel. Someone argues: "a spherical cavity is the shape closest to a real molecular gap, so the sphere reading is the one true field inside the dielectric. The needle and disc readings are just approximations to this true value, and if computed correctly they should agree with it."
((a)) Compute the field a probe would read in a needle-shaped cavity drilled along E, in a spherical cavity, and in a thin disc-shaped cavity cut across E.
((b)) Explain what is wrong with the claim.