The wide prong is neutral on 15 amp US power outlets.
Is there a reason it was designed this way, or could the narrow slot just as easily have been neutral instead? Was this design decision arbitrary?
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I don't know a definitive historical answer. From an electrical perspective there's no reason to prefer one over the other, at least once the connection is made.
There are two potential reasons I can think of:
1) If the plug is only partially inserted (or has been slowly falling out), the wider prong may be more likely to make contact. If only one of the two is connected, it's safer for it to be the neutral one.
2) If a child happens to pick up a paperclip or some other bit of metal and decides to stick it in the plug, there's a chance it will only fit in the larger of the two slots, or maybe psychologically they would tend to choose the larger of the two slots. Don't rely on this!