We present a simple analytical expression of plasma density by making use of the electron density equation to study the dynamic behavior of the corona discharge plasma. It assumes that a specified voltage profile is fed through the inner conductor of the reactor chamber consisting of two coaxial conducting cylinders. The analytical description is based on the electron continuity equation with ionization and attachment by electrons. It is found that the electron density profile calculated between two coaxial cylindrical electrodes depends very sensitively on the Profile of applied voltage. The analytical expression of plasma density and its generation will provide important scaling laws in the corona discharge plasma.