Conductive particles greatly impair the insulation integrity of a gas insulated switchgear (GIS). Factors including applied voltage, frequency of the alternating current, size and coefficient of restitution of the metallic particle, pressurized gas, and sizes of the GIS dramatically influence the particle dynamics. Previous investigations basically focused on certain scenarios, seldom considered the effects from coefficient of restitution, and did not provide universal laws for the particle dynamics. This paper proposes a dimensionless number that considers all the above-mentioned factors, and presents the scaling law between dimensionless mean/maximum lifting height of a charged particle in GIS and the proposed dimensionless number. It is believed that the scaling law together with the dimensionless number can provide guidance and shrink the parameter window for relevant investigations on the GIS with sparsely distributed conductive particles.