All Problems

Electric Current

Problem 3.202

A cylindrical capacitor connected to a dc voltage source \(V\) touches the surface of water with its end (Fig. 3.56). The separation \(d\) between the capacitor electrodes is substantially less than their mean radius. Find a height \(h\) to which the water level in the gap will rise. The capillary effects are to be neglected.

Reveal Answer
h1/2ε0(ε1)V2/ρgd2, where ρ is the density of water. h \approx 1 / 2 \varepsilon_{0}(\varepsilon-1) V^{2} / \rho g d^{2}, \text { where } \rho \text { is the density of water. }