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AP Physics C: E&M
10.4 Dielectrics
10.3 Capacitors
IntermediateMCQProportional AnalysisConceptual24.2k
Cross section of the parallel-plate capacitor completely filled with a dielectric slab of constant \(\kappa\).
Cross section of the parallel-plate capacitor completely filled with a dielectric slab of constant \(\kappa\).
A parallel-plate capacitor with vacuum between its plates has plate area \(A\), plate separation \(d\), and free surface charge density of magnitude \(\sigma_0\) on each plate. The capacitor is disconnected from the charging source, and an uncharged dielectric slab of dielectric constant \(\kappa > 1\) is inserted to completely fill the space between the plates.

Net Electric Field \(E\)Induced Surface Charge Density \(\sigma_{\text{ind}}\)Stored Electrostatic Energy \(U\)
(A)\(\dfrac{E_0}{\kappa}\)\(\sigma_0\left(1 - \dfrac{1}{\kappa}\right)\)\(\dfrac{U_0}{\kappa}\)
(B)\(\dfrac{E_0}{\kappa}\)\(\dfrac{\sigma_0}{\kappa}\)\(\dfrac{U_0}{\kappa}\)
(C)\(\dfrac{E_0}{\kappa}\)\(\sigma_0\left(1 - \dfrac{1}{\kappa}\right)\)\(\kappa U_0\)
(D)\(E_0\)\(\sigma_0(\kappa - 1)\)\(U_0\)

Which row in the table correctly compares the resulting net electric field magnitude \(E\), the induced surface charge density magnitude \(\sigma_{\text{ind}}\) on the dielectric faces, and the stored electrostatic energy \(U\) to their initial values \(E_0\), \(\sigma_0\), and \(U_0\)?

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