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Method of Images

The method of images, introduced by Lord Kelvin in 1848, is commonly used to determine VDescription: 29053.pngDescription: 28731.png and Description: 28503.png due to charges in the presence of conductors.


The image theory states that a given charge configuration above an infinite grounded perfect conducting plane may be replaced by the charge configuration itself, its image, and an equipotential surface in place of the conducting plane.


For image theory, two conditions must be satisfied:
  1. The image charge(s) must be located in the conducting region.
  2. The image charge(s) must be located such that on the conducting surface(s) the potential is zero or constant.
Definition of Images
The fictitious charges, placed in the region where the field is not required and producing the same field in the desired region as with the actual electrification of the surface, are defined as the electrical images.


Suppose we have a conducting surface in the vicinity of one or more point charges. The point charge will induce charges on the conducting surface.
Our purpose is to find the potential and field in the space outside the conductor not occupied by the charges. In this region, Laplace’s equation is satisfied with suitable boundary conditions.
In the method of images, the actual electrification of the surface is replaced by one or more fictitious point charges in the region where the field or potential is not desired. The positions and the magnitudes of these fictitious charges are such that in the desired region, Laplace’s equation is satisfied with the same conditions.
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Image systems: (a) Charge configurations in the presence of perfectly conducting plane (b) Image configurations
For example, the method of images suggests that for a point charge +Q at a point (0, 0, d), an exactly equal and opposite charge -Q is assumed to exist at the point (0, 0, -d); replacing the conducting plane by an equipotential surface with zero potential. Typical examples of point, line and volume charge configurations are shown in Fig.(a) and their images are shown in Fig.(b)
By the method of images,
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We consider the following examples using method of images.

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