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Asked in GSEB Board July 2015 · Magnetic moment of magnets and loops
Given: a straight wire of length l with moment m=qₘl, where qₘ is its pole strength.
Idea: bending keeps the pole strength and keeps the length of the wire. Only the straight-line distance between the poles changes, and the moment is pole strength times that distance.
Semicircle: the arc is the whole wire, so π R=l and R=l/π.
The poles end up at opposite ends of a diameter, 2R=(2l)/π apart.
m'=qₘ×(2l)/π=2/π(qₘl)=(2m)/π.
Since 2/π≈0.64, the bent wire is the weaker magnet, as it should be.
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