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Asked in GUJCET 2011 · Magnetic moment of magnets and loops
Given: a straight magnetised wire of length L and pole strength qₘ, so its moment is m=qₘL=4π A m².
Idea: bending changes neither the pole strength nor the length of the wire. It only brings the two poles closer, and the moment is pole strength times the straight-line distance between them.
Bent into a semicircle of radius R, the arc is the whole wire: π R=L, so R=L/π.
The poles now sit at the two ends of a diameter, a distance 2R=(2L)/π apart.
New moment m'=qₘ(2R)=qₘL·2/π=(2m)/π.
With m=4π: m'=(2×4π)/π=8 A m².
That value is not among the first three options, so the answer is None of these.
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