Magnetic moment of current loop integral

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The discussion centers on the calculation of the magnetic moment of a current loop, specifically questioning the use of the line integral notation. The original expression ∮ r x dr is scrutinized, with the argument that dr should not be used since it aligns with r, making the cross product invalid. Instead, the notation ∮ r x dl is proposed as more appropriate, where dl represents a small change along the loop. This highlights a potential notation error in the original formulation. Clarifying the correct notation is essential for accurate calculations in magnetic moment analysis.
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The question states: The calculation of the magnetic moment of a current loop leads to the line integral
∮ r x dr
I am puzzled - shouldn't this be ∮ r x dl where r is the radius of the loop and dl is the small change along the loop?
(I think dr would be in the same direction as r, so no cross product for r and dr?)
 
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That looks like a notation error. r x dl looks better.
 
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