kuvamenetelmä

Kuvamenetelmä, often translated as "image method" or "picture method," is a mathematical technique used primarily in electromagnetism and electrostatics to solve boundary-value problems. It involves introducing fictitious charges, known as "image charges," in positions outside the actual charge distribution and boundary to simplify the problem. These image charges are chosen such that they satisfy the boundary conditions of the original problem.

The core idea is to replace a complex physical setup, such as a point charge near a conducting plane, with a simpler, mathematically equivalent system. In the case of a point charge above an infinite conducting plane, an image charge of equal magnitude and opposite sign is placed at an equal distance behind the plane. This configuration then produces an electric potential and field that exactly matches the original problem in the region of interest (i.e., above the conducting plane).

This method is particularly effective for problems involving conductors, such as planes, spheres, and cylinders, due to the property that the electric potential on a conductor is constant. By strategically placing image charges, the boundary condition of constant potential on the conductor is satisfied, allowing for straightforward calculation of the electric field and potential in the rest of space. The force on the original charge can then be calculated as the force between the original charge and its image charge. While conceptually simple, the application of the image method can become more complex for intricate geometries or multiple boundaries.