Question #42668

A uniform electric field $\vec{E}_1$ exists in a vacuum region ($y > 0$). The electric field lines make an angle $\theta_1 = 60^\circ$ with the normal to the $x$-$z$ plane (the $y$-axis). The region $y < 0$ is filled with a linear, isotropic dielectric material of dielectric constant $K = 3$. There is no free charge on the boundary interface at $y = 0$. Let $d_1$ (in meters) and $d_2$ (in meters) be the perpendicular distances between two adjacent equipotential surfaces separated by the same potential difference $\Delta V$ (in volts) in the vacuum and the dielectric, respectively. Due to the surface polarization charge density at the interface, the equipotential surfaces exhibit a geometric 'kink'. Calculate the ratio $\frac{d_2}{d_1}$.