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Conductors and Dielectrics in an Electric Field

Problem 3.88

A. uniform electric field of strength E=100 V/mE=100 \mathrm{~V} / \mathrm{m} is generated inside a ball made of uniform isotropic dielectric with permittivity ε=5.00.\varepsilon=5.00 . The radius of the ball is R=3.0 cm.R=3.0 \mathrm{~cm} . Find the maximum surface density of the bound charges and the total bound charge of one sign.

Reveal Answer
 3.88. σmax⁡′=(ε−1)ε0E=3.5nC/m2,q′=πR2(ε−1)ε0E==10pC.\begin{aligned} & \text { 3.88. } \sigma_{\max }^{\prime}=(\varepsilon-1) \varepsilon_{0} E=3.5 \mathrm{nC} / \mathrm{m}^{2}, q^{\prime}=\pi R^{2}(\varepsilon-1) \varepsilon_{0} E=\\ =& 10 \mathrm{pC} . \end{aligned}
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