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title: "A parallel-plate capacitor with plate separation \\(d\\) and vacuum capacitance \\(C_0\\) is connected to an ideal battery of potential difference \\(V_0\\), and the circuit is allowed to reach steady state. A slab of dielectric material with dielectric constant \\(\\kappa > 1\\), designed to completely fill the region between the plates, is then fully inserted into the capacitor while the battery remains connected. Which of the following statements correctly describes the change in the magnitude of the charge stored on each plate and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/124774/"
date_modified: "2026-09-28T14:11:12+00:00"
---

# A parallel-plate capacitor with plate separation \(d\) and vacuum capacitance \(C_0\) is connected to an ideal battery of potential difference \(V_0\), and the circuit is allowed to reach steady state. A slab of dielectric material with dielectric constant \(\kappa > 1\), designed to completely fill the region between the plates, is then fully inserted into the capacitor while the battery remains connected. Which of the following statements correctly describes the change in the magnitude of the charge stored on each plate and provides the correct physical justification?

A parallel-plate capacitor with plate separation \(d\) and vacuum capacitance \(C_0\) is connected to an ideal battery of potential difference \(V_0\), and the circuit is allowed to reach steady state. A slab of dielectric material with dielectric constant \(\kappa > 1\), designed to completely fill the region between the plates, is then fully inserted into the capacitor while the battery remains connected. Which of the following statements correctly describes the change in the magnitude of the charge stored on each plate and provides the correct physical justification?

![A circuit diagram consisting of a single rectangular loop oriented horizontally. The left vertical branch contains an ideal battery labeled \(V_0\), with a longer horizontal line on top representing the positive terminal and a shorter, thicker horizontal line below representing the negative terminal. The top and bottom horizontal segments are straight conducting wires. The right vertical branch contains a parallel-plate capacitor composed of two horizontal parallel lines of equal length separated by a gap of width \(d\). A shaded rectangular slab labeled \(\kappa\) is shown partially inserted between the two plates from the right, with a straight horizontal arrow pointing to the left toward the interior of the plates. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604672-k0Y39I.jpg)

- **A.** The magnitude of the charge stored on each plate increases by \(\kappa C_0 V_0\) because the dielectric reduces the effective plate separation, causing the battery to supply enough charge to establish a final electric field of magnitude \(\kappa V_0/d\) between the plates.
- **B.** The magnitude of the charge stored on each plate increases by \((\kappa - 1)C_0 V_0\) because bound surface charges in the polarized dielectric partially shield the free charges, requiring additional free charge from the battery to restore the potential difference across the plates to \(V_0\).
- **C.** The magnitude of the charge stored on each plate decreases by \(\left(1 - \dfrac{1}{\kappa}\right)C_0 V_0\) because the polarization field within the dielectric opposes the external field, driving positive charge back into the positive terminal of the battery until the field drops to \(V_0/(\kappa d)\).
- **D.** The magnitude of the charge stored on each plate stays the same because the battery maintains a constant potential difference \(V_0\) across the plates, and the transient current merely redistributes charge between the plates and the dielectric without altering the net free charge.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124774/*