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AP Physics C: E&M
10.4 Dielectrics
10.3 Capacitors
AdvancedMCQMathematical17.3k
A side view of a parallel-plate capacitor with two horizontal parallel rectangular plates of length L separated vertically by distance d. A rectangular dielectric slab of length L and thickness d is partially inserted from the left between the plates to a distance x. The region of length x containing the dielectric is shaded gray. The remaining region of length L minus x between the plates is unshaded white space representing vacuum. A horizontal dashed coordinate axis x extends along the bottom plate, with origin x equals 0 at the left edge of the plates and x equals L at the right edge. No other labels, lines, text, or axes appear.
A dielectric slab partially inserted distance x into a parallel-plate capacitor.
An isolated parallel-plate capacitor with square plates of side length \(L\) and plate separation \(d\) holds a fixed positive charge \(Q\). A dielectric slab with dielectric constant \(\kappa\) and thickness \(d\) is inserted a distance \(x\) into the capacitor (\(0 < x < L\)). Let \(C_0 = \dfrac{\varepsilon_0 L^2}{d}\) be the capacitance of the empty capacitor. Which of the following expressions gives the magnitude of the electrostatic force exerted on the dielectric slab by the capacitor's electric field as a function of \(x\)?

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