| MadSci Network: Physics |
In water, electric current appears when 3D fields of underwater electric voltage drive charged atoms forward. (In water the atoms are commonly the sodium ions and chloride ions). The current follows the voltage field, and the voltage field between two small metal objects is shaped a bit like the field between two unlike magnetic poles. We can easily visualize its shape by imagining that WATER rather than electric charges is flowing between the appliance and the metal bathtub drain.
Imagine that we drop a hair dryer into the tub, and the hair dryer starts spewing out water very slowly. At the same time the plug in the bathtub drain starts leaking. A slow water current would result. This current would NOT be shaped like a narrow beam that moves from appliance to bathtub drain. Instead, the water would spread in all directions from the appliance, the entire liquid contents of the bathtub would slowly move away from the appliance and towards the drain, and the flow would slowly contract inwards and ooze past the drain plug. There would be no spot in the bathtub where the water stayed still. If the appliance fell very close to the drain, then yes, the fastest current would exist between them. Other parts of the tub would experience lower (but not zero) flow.
Electric current takes a similar path. Charges in all parts of the tub are sucked towards the drain, and at the same time they are pushed away from the appliance. All the charges in the water are driven into motion, and an electric current appears everywhere. (For AC, the flow wiggles back and forth, but its path is the same.) A human body contains salt water and is a good conductor. Human skin is resistive unless it has been soaked in water for a time, so human skin is usually conductive too. A human body in the tub is therefor transparent to the flow of electric charges. No matter where you stick your body, it will intercept a portion of the flowing charge. If you are sitting in the tub, the current interferes with nerve signals, makes muscles clench, and quickly causes breathing to stop.
Another point: fiberglass bathtubs have only one metal connection at the drain, but older tubs are all metal. The porcelain coating is insulating, but if it has many small pores, then the path of charge-flow will be between the appliance and the entire tub, and not just between the appliance and the metal drain, and there won't be anywhere to hide from the path of the current
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