Question 2.42: Two grounded semi infinite metallic plates are placed on the...
Two grounded semi infinite metallic plates are placed on the x axis and the y axis of a Cartesian coordinate system in order to form a 90° corner. A positive charge 4πεo is located at the point (a, a) where a is arbitrary. Using MATLAB, carefully plot equipotential contours surrounding this charge and the expected electric field.
There will be 2 negative image charges located at the points (a, -a) and (-a, a). In addition, there will be a positive image charge at (-a, -a) since the electric potential at all points of the metallic corner must be equal to 0. This system of four alternative charges is often called a “quadripole”. The results of the calculation are shown below. We find that the electric field is always perpendicular to the metal surfaces. This indicates that the metallic surfaces are equipotential contours that have a value equal to 0.
In high-energy particle experiments in which charged particles move through a metallic tube and are to collide together, the experimentalist must be aware of these image charges. The image charges can be found for cases only when the corner has an angle that is a submultiple of 2π.
