Linear superposition of fields

This equation shows an additive relation between the potentials and therefore fits a fundamental principle of electrostatics the linear superposition of fields. 

This may contradict one of the basic laws of electrostatics, that is the linear superposition of fields. This is a fundamental problem for the theory and to any other theory or development, such as that due to Guggenheim below (Section 10.13.1), which makes use of any such combination. In fact this is one of the big problems in the theory. The other big problem is that the x/tjS in the Poisson equation and in the Maxwell-Boltzmann distribution are different and have a different physical basis (see Section 10.6.5). This is believed by many to be yet another fundamental problem for the theory. 

This is serious even though it removes the problem of the linear superposition of fields by having both sides of the combined equation linear. But it imposes a very severe restriction to the theory because the approximation requires... 

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