A straight steel wire of length 2 units has magnetic dipole moment of m and the wire is bent in the form of a semicircle, the new value of magnetic dipole moment is unit.

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(2) (2m)/π. Given: straight length L=2 units with moment m=qₘL=2qₘ, so the pole strength is qₘ=m/2. Idea: bending changes neither the pole strength nor the length of the wire, only the straight-line distance between the poles. Semicircle of radius R: the arc is the whole wire, π R=2, so R=2/π. The poles are now at the ends of a diameter, 2R=4/π apart. New moment m'=qₘ(2R)=m/2×4/π=(2m)/π. The ratio (m')/m=2/π≈0.64 holds for a wire of any length -- the given length 2 cancels out.

A straight steel wire of length 2 units has magnetic dipole moment of m and the wire is bent in the form of a semicircle, the new value of magnetic dipole moment is ______ unit.

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