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Conductors and Dielectrics in an Electric Field

Problem 3.98

A uniform dielectric ball is placed in a uniform electric field of strength E0.\mathbf{E}_{0} . Under these conditions the dielectric becomes polarized uniformly. Find the electric field strength E inside the ball and the polarization P\mathbf{P} of the dielectric whose permittivity equals ε\varepsilon. Make use of the result obtained in Problem 3.96.

Reveal Answer
E=3E0/(ε+2),P=3ε0E0(ε−1)/(ε+2)\mathbf{E}=3 \mathbf{E}_{0} /(\varepsilon+2), \mathbf{P}=3 \varepsilon_{0} \mathbf{E}_{0}(\varepsilon-1) /(\varepsilon+2)
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