A point charge in front of a grounded metallic corner.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. 

A point charge in front of a grounded metallic corner with dimensions etc.

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.

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