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title: "Two long vertical parallel conducting plates of width \\(w\\) and separation \\(d\\) are connected to a constant voltage source supplying potential difference \\(V_0\\). The lower ends of the plates are submerged in a reservoir containing an insulating liquid of mass density \\(\\rho\\) and dielectric constant \\(\\kappa\\). Electrostatic forces draw the liquid upward between the plates to an equilibrium height \\(h\\) above the surface of the external reservoir. Which of the following expressions correctly gives the equilibrium height \\(h\\)?"
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url: "https://nerd-notes.com/ubq/118287/"
date_modified: "2026-08-04T08:08:42+00:00"
---

# Two long vertical parallel conducting plates of width \(w\) and separation \(d\) are connected to a constant voltage source supplying potential difference \(V_0\). The lower ends of the plates are submerged in a reservoir containing an insulating liquid of mass density \(\rho\) and dielectric constant \(\kappa\). Electrostatic forces draw the liquid upward between the plates to an equilibrium height \(h\) above the surface of the external reservoir. Which of the following expressions correctly gives the equilibrium height \(h\)?

Two long vertical parallel conducting plates of width \(w\) and separation \(d\) are connected to a constant voltage source supplying potential difference \(V_0\). The lower ends of the plates are submerged in a reservoir containing an insulating liquid of mass density \(\rho\) and dielectric constant \(\kappa\). Electrostatic forces draw the liquid upward between the plates to an equilibrium height \(h\) above the surface of the external reservoir. Which of the following expressions correctly gives the equilibrium height \(h\)?

![A schematic diagram showing two parallel vertical metal plates, each of height L, separated horizontally by a distance d. The lower ends of both plates are submerged in a dielectric liquid reservoir. Between the plates, the liquid column rises to a vertical height h above the surrounding liquid level outside the plates. An ideal DC battery labeled V_0 is connected by straight horizontal wires to the top of the two plates. A vertical double-headed arrow labeled h measures the vertical distance from the free liquid surface outside the plates to the top of the liquid column inside the plates. A horizontal arrow labeled d indicates the spacing between the inner faces of the two plates. No other labels, lines, symbols, or background elements appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830921-V4JZ4e.jpg)

- **A.** \(h = \dfrac{\varepsilon_0 (\kappa - 1) V_0^2}{\rho g d^2}\)
- **B.** \(h = \dfrac{\kappa \varepsilon_0 V_0^2}{2 \rho g d^2}\)
- **C.** \(h = \dfrac{\varepsilon_0 (\kappa - 1) V_0^2}{2 \rho g d^2}\)
- **D.** \(h = \dfrac{\varepsilon_0 (\kappa - 1) V_0^2}{2 \kappa \rho g d^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118287/*