<![CDATA[Silent discharge is well known method to initiate plasma reaction because initial discharge is easily triggered by implementing high voltage to the pair of coupled electrodes with a distance. However, it is very difficult to determine the exact amount of the voltage that initiates the discharge. There are many factors influence the condition of initial discharge such as dimensions, type and geometrical shapes of electrode, thickness of insulation, and type of electric field inside the gap between the electrodes. To obtain lower initial discharge voltage, it is urgent to find the best electrode shape producing electric field contours in line with electron emission triggering. This work examines the behavior of electric field and the applied voltage surrounding electrodes by investigating the mathematical expression for given voltage and generated electric field. The mathematical relationship then gives a basis of theoretical background for electric field contours of two shape electrodes. It is also well known that among many electrodes, the non-uniform geometrical shape is preferred to initiate electric field easily. In this study, a hole shape and a bulge type electrode are investigated.Keywords: silent discharge, electric field, differential equation, electrode shape ]]>
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