The **method of image charges** is a powerful technique to find the **electrostatic potential** in an intuitive way. In this problem you will find out how it can be applied to a point charge close to two grounded intersecting metallic half-planes.

## Problem Statement

A point charge \(q\) shall be close to two grounded and orthogonal **metallic half-planes** at \(\mathbf{r}_q = \left(d_x,d_y,0\right)\). Calculate the **electrostatic potential** \(\phi\left(\mathbf{r}\right)\) and the **force** acting on the charge using the **method of image charges**! Could this method be used if the angle \(\alpha\) between the half-planes would be different? Consider the case of \(\alpha = 60^{\circ}\).

## Background: Enhanced Radiation of Molecules

Even if this problem might be very old, we can still learn a lot from it. Imagine for example a **molecule** in front of a real metal that allows some penetration of the field. Here, a perfect conductor may still be a very good **approximation** and one can find the scattered field of the molecule at its very position. This field causes a change of the **radiative decay rates** of the molecule, a kind of self-induced emission called the **Purcell Effect**. This effect is of particular importance to understand applications as the surface enhanced Raman spectroscopy.