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A conducting wire of 1 m length is used to form a circular loop. If it carries a current of 1 ampere, its magnetic moment will be ______ A m².

Asked in GSEB Board July 2015 · Magnetic moment of loops and charges

• (1) 2π
• (2) π/2
• (3) π/4
• (4) 1/(4π)

Step-by-step solution

Why the other options are wrong

• (1) 2π is the circumference of a circle of radius 1 m, not an area. Here the 1 m of wire is itself the circumference, which leaves a radius of only 1/(2π)≈0.16 m. Sanity check: m=IA=1/(4π)≈0.08 A m².
• (2) No single slip gives π/2≈1.57. Sanity check: the loop's radius is 1/(2π)≈0.16 m, so it encloses about 0.08 m² and with I=1 A the moment is about 0.08 A m².
• (3) π/4 comes from taking the 1 m wire as the diameter of the loop: r=0.5 m gives A=π r²=π/4. The wire's length is the circumference, 2π r=1 m.

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