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Potential calculations

The potential can in general be calculated by dividing the present distribution of charges into small elements that are each to be considered as point charges. The potential in a given point of space can then be calculated by a summation of the contributions of all point charges.

There are two disadvantages of this method:

bulletSometimes the distribution of charges is not known. 
For example, electrical conductors that are connected to a voltage source do have a well-defined potential, however,  that does not mean that the precise distribution of charges along the conductor is known.
bulletIn case of non-symmetric or otherwise complicated distributions of charges the summation of the contributions from all point charges may require a non-trivial integration task.

An alternative: the relaxation method. This is a numerical method, i.e., usually the computation has to be performed by a computer. 

bulletWhen can the relaxation method be applied?
bulletHow does the relaxation method work?
bulletWhy does the relaxation method give the correct potential?

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Last change: October 09, 2001