Two large parallel conducting plates a distance apart are joined by a wire of zero…
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
Two large parallel conducting plates a distance d apart are joined by a wire of zero resistance, so that they are at the same potential, and the pair is isolated and initially uncharged. An electret slab of thickness t (t<d) with a fixed uniform polarisation P perpendicular to its faces lies in the gap with its faces parallel to the plates; the rest of the gap is vacuum. Take the x axis along P, from the left plate at x=0 to the right plate at x=d. The plates are large enough that edge effects are ignored, so every field is along x and uniform within each region.
((a)) Using Gauss's law for D, show that Dx has the same value in the vacuum and in the slab, and that this value equals the free surface charge density σf on the inner face of the left plate.
((b)) Using the fact that the two plates are at the same potential, show that Dx=Pt/d, and hence obtain expressions for Ex in the vacuum region and in the slab.
((c)) Evaluate Dx, and Ex in each region, for P=4.0×10−6Cm−2, t=2.0mm and d=5.0mm, and state the direction of the field inside the slab relative to P.