Method of Image Charges: Point Charge inside a Planar Capacitor

The electrostatic problem of a point charge inside a capacitor made of two parallel grounded electrodes is illustrated in this Demonstration. The electric potential and field can be calculated as an infinite sum of image charges. On the left you see the space between the two parallel plates represented by horizontal red lines. Move the point charge and view the resulting electric field (blue stream-lines) and equipotential lines (black). On the right, you can see the set of real and image charges (red for positive, blue for negative) as well as the location of the two real plates (solid red lines) and several of their images (dashed gray lines).

The method of image charges is one of the basic tools for the solution of electrostatic problems. Given a set of charges and boundary conditions, the method finds image charges outside the problem domain, creating a potential that, when added to the one created by the real charges, fulfills the boundary conditions. The resulting potential is a solution of the problem since the solution of Poisson's equation inside a domain is unique, given the distribution of charges inside and the potential at the boundary.

This Demonstration illustrates the method of image charges by finding the electrostatic potential and the electric field created by a charge between two parallel grounded electrodes. In this case the problem is solved by an infinite sum of charges that have to be truncated. You can see how the solution converges by including more and more image charges in the sum. In the exact solution the equipotential lines are parallel to the electrodes while the field is perpendicular to them.