Complete the comparison between the three symmetric magnetostatic geometries.
The field of a long straight wire falls as one over the ______, the field inside a long solenoid is ______ across the bore, and the field inside a toroid falls as one over the ______, so a toroid, unlike a solenoid, needs a stated ______ before its field means anything.
Word bank: distance · uniform · radius · position · current
Hints
- Each geometry follows from Ampere’s law with a different choice of loop.
- Two of the blanks describe the same kind of falloff, at different scales.
Show the answer
The field of a long straight wire falls as one over the distance, the field inside a long solenoid is uniform across the bore, and the field inside a toroid falls as one over the radius, so a toroid, unlike a solenoid, needs a stated position before its field means anything.
The wire gives , the solenoid a uniform , and the toroid . Because the toroid’s field varies across the bore, quoting it without a radius is meaningless, a distinction that catches people out.
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