All Problems Electric Capacitance, Energy of an Electric Field
Problem 3.103
The space between the plates of a parallel-plate capacitor is filled consecutively with two dielectric layers 1 and 2 having the thicknesses \(d_{1}\) and \(d_{2}\) and the permittivities \(\varepsilon_{1}\) and \(\varepsilon_{2}\) respectively The area of each plate is equal to \(S .\) Find: (a) the capacitance of the capacitor; (b) the density \(\sigma^{\prime}\) of the bound charges on the boundary plane if the voltage across the capacitor equals \(V\) and the electric field is directed from layer 1 to layer 2 .
(a) \(C=\frac{\varepsilon_{0} S}{d_{1} / \varepsilon_{1}+d_{2} / \varepsilon_{2}}\); (b) \(\sigma^{\prime}=\varepsilon_{0} V \frac{\varepsilon_{1}-\varepsilon_{2}}{\varepsilon_{1} d_{2}+\varepsilon_{2} d_{1}}\).