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A current I flows in a conducting wire of length L. If we bend it in a circular form, its magnetic dipole moment would be ______.

Asked in GUJCET 2008 · Magnetic moment of loops and charges

• (1) (I²L)/(4π)
• (2) (I²L²)/(4π)
• (3) (IL²)/(4π)
• (4) (IL)/(4π)

Step-by-step solution

Why the other options are wrong

• (1) m=IA is first order in the current, so I² cannot appear. The units say the same thing: this is A² m, while a magnetic moment is A m².
• (2) Here both factors have been squared. Only the length is squared, because the area π r² carries two powers of L; the current enters just once through m=IA.
• (4) This takes the area of the loop to be L itself. The wire of length L becomes the circumference, so r=L/(2π) and the area is π r²=(L²)/(4π) — one more power of L than this option has.

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