Consider a capacitor with two parallel plates separated by a distance \( d \). The capacitor is immersed vertically in a dielectric fluid with a dielectric constant \( K \) and density \( \rho \). Determine the height to which the fluid rises between the plates when the capacitor is connected to a battery that maintains a constant voltage \( V \) across the plates.
1
\( h = \frac{V^2 (K - 1)}{2\pi \rho g d^2} \)
2
\( h = \frac{V^2 (K - 1)}{4\pi \rho g d^2} \)
3
\( h = \frac{V^2 (K - 1)}{6\pi \rho g d^2} \)
4
\( h = \frac{V^2 (K - 1)}{8\pi \rho g d^2} \)