Simulation of electric fields using symmetrically placed charges

The electric fields associated with sphere-plane gap geometry is simulated using charge simulation method (CSM). In the present study simulation results with symmetrical placed 6 and 14 point charges are reported. The errors in charge simulation method (CSM) of sphere surface potentials are analyzed by optimally placing the charges. The optimal location of point charges used in simulation are identified using genetic algorithm (GA). The GA makes use of maximum-potential-error on the surface of the sphere electrode as the objective function in identifying optimal charge locations. A large number of numerical experiments are conducted and surface error plots are reported. The effort here has been to see the effect of optimally and symmetrically placed charges on simulation error. Results indicate that percentage maximum potential errors in simulation on the surface got reduced from 3.86e-004 to 1.30e-005 when the number of charges is increased from 6 to 14, respectively (with optimal locations). It is known from the literature that increasing the number of charges improves results of simulation in CSM. Application of GA in conjunction with CSM have been some of the recent efforts and the present work brings out the point that non optimally located increased number of charges may not yield results with improvement in accuracy.