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Conductors and Dielectrics in an Electric Field

Problem 3.100

A long round cylinder made of uniform dielectric is placed in a uniform electric field of strength E0.\mathbf{E}_ {0} . The axis of the cylinder is perpendicular to vector E0\mathbf{E}_{0}. Under these conditions the dielectric becomes polarized uniformly. Making use of the result obtained in the foregoing problem, find the electric field strength E\mathbf{E} in the cylinder and the polarization P\mathbf{P} of the dielectric whose permittivity is equal to ε\varepsilon.

Reveal Answer
E=2E0/(ε+1);P=2ε0E0(ε−1)/(ε+1)\mathbf{E}=2 \mathbf{E}_{0} /(\varepsilon+1) ; \mathbf{P}=2 \varepsilon_{0} \mathbf{E}_{0}(\varepsilon-1) /(\varepsilon+1)
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