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Conductors and Dielectrics in an Electric Field

Problem 3.84

Initially the space between the plates of the capacitor is filled with air, and the field strength in the gap is equal to \(E_{0}\). Then half the gap is filled with uniform isotropic dielectric with permittivity \(\varepsilon\) as shown in Fig. \(3.12 .\) Find the moduli of the vectors \(\mathbf{E}\) and \(\mathbf{D}\) in both parts of the gap \((1\) and 2\()\) if the introduction of the dielectric (a) does not change the voltage across the plates; (b) leaves the charges at the plates constant.

Reveal Answer
 3.84. (a) E1=2εE0/(ε+1),E2=2E0/(ε+1),D1=D2==2εε0E0/(ε+1); (b) E1=E0,E2=E0/ε,D1=D2=ε0E0\begin{array}{l} \text { 3.84. (a) } E_{1}=2 \varepsilon E_{0} /(\varepsilon+1), E_{2}=2 E_{0} /(\varepsilon+1), D_{1}=D_{2}= \\ =2 \varepsilon \varepsilon_{0} E_{0} /(\varepsilon+1) ; \text { (b) } E_{1}=E_{0}, E_{2}=E_{0} / \varepsilon, D_{1}=D_{2}=\varepsilon_{0} E_{0} \end{array}
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