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In this paper we measured quench-induced dynamic breakdown strength of liquid helium (LHe) under various quench environment of superconducting (SC) coils for electrical insulation design of SC power equipment. Experimental results revealed that the dynamic breakdown strength of LHe drastically decreased with even small post-quench thermal energy of SC coils. However, the dynamic breakdown strength was improved with the increase in the pressure of LHe because of the suppression of thermal bubble disturbance in LHe. Moreover, we established 3-dimensional diagrams of the dynamic breakdown strength of LHe as a function of effective post-quench thermal energy density and pressure of LHe. The diagrams are applicable to the practical insulation design of SC equipment under quench environment.