Dirichlet’s problem

Fig. 1.8. (a) Dirichlet s problem, (b) Neumann s problem, (c) the third boundary value problem. 

The solution for this equation is the same as that of the constant potential boundary conditions (Dirichlet s problem) and was solved not only for electrostatic fields but also for heat fluxes and concentration gradients (chemical potentials) [10]. The primary potential distribution between two infinitely parallel electrodes is simply obtained by a double integration of the Laplace equation 13.5 with constant potential boundary conditions (see Figure 13.3). The solution gives the potential field in the electrolyte solution and considering that the current and the electric potential are orthogonal, the direct evaluation of one function from the other is obtained from Equation 13.7. 

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