An electric charge trapped in polymeric insulating material makes an ultra high electric field of 500 to 2000 kV/mm within 10 angstrom near trapped charge, that the electric field intensities have been calculated by the classical theory of Coulomb' law. This paper discusses the both of Fermi level and electrical potential distribution near trapped charge area by using the classical theory (Coulomb' law) and the quantum theory (electron wave function). It is found that the quantum theory is dominant within about 7.7 angstrom near trapped charge. Both of the classical and quantum theory should be considered a region 7.7 to 25 angstrom and there is ultra high electric field of 500 kV/mm to 2000 kV/mm in this region.