Build up static charge and trigger a spark discharge
When a shoe rubs against carpet, electrons transfer from carpet to shoe (or vice versa) due to the triboelectric effect. The accumulated charge creates a voltage across the body. When this voltage is high enough (air breakdown at ~3 MV/m), a spark discharges the built-up charge through the ionized air path. Humidity allows gradual charge leakage, reducing maximum charge buildup.
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