Table: induction_materials
Columns: material
resistivity_10_6_ohm_inches
relative_permeability
skin_depth_inches
surface_resistance_relative_to_copper

Question: What is the lowest relative permeability with a skin depth larger than 0.112 inches?
SQL: SELECT MIN("relative_permeability") FROM induction_materials WHERE "skin_depth_inches" > 0.112

Question: What is the average relative permeability with a resistivity smaller than 1.12 and a surface resistance relative to copper smaller than 1?
SQL: SELECT AVG("relative_permeability") FROM induction_materials WHERE "resistivity_10_6_ohm_inches" < 1.12 AND "surface_resistance_relative_to_copper" < 1

Question: What is the sum of skin depth with a resistivity of 1.12 and a relative permeability larger than 1?
SQL: SELECT SUM("skin_depth_inches") FROM induction_materials WHERE "resistivity_10_6_ohm_inches" = 1.12 AND "relative_permeability" > 1