In the local field problem the cavity need not be chosen as spherical,

1.	In the local field problem the cavity need not be chosen as spherical, but may be of any shape possessing at least cubic symmetry. We may for example take the cavity as a cube with a face normal parallel to the polarization. In this case the polarization charge density on the upper and lower faces of the cube is uniform and equal to +P, while the other faces do not carry any charge. Show that, for this cavity, E2=4mP/3, just as for the spherical cavity.
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In the local field problem the cavity need not be chosen as spherical, but may be of any shape possessing at least cubic symmetry. We may for example take the cavity as a cube with a face normal parallel to the polarization. In this case the polarization charge density on the upper and lower faces of the cube is uniform and equal to +P, while the other faces do not carry any charge. Show that, for this cavity, E2=4mP/3, just as for the spherical cavity.

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