Magnetic moment of current loop integral

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SUMMARY

The discussion centers on the calculation of the magnetic moment of a current loop, specifically addressing the line integral representation. The integral is correctly expressed as ∮ r x dl, where r represents the radius of the loop and dl denotes the differential length element along the loop. The original notation using dr is identified as a potential error, as dr would align with r, negating the cross product. This clarification is essential for accurate calculations in electromagnetism.

PREREQUISITES
  • Understanding of vector calculus, particularly cross products.
  • Familiarity with electromagnetism concepts, specifically magnetic moments.
  • Knowledge of line integrals in physics.
  • Basic principles of current loops in magnetic fields.
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  • Study vector calculus applications in electromagnetism.
  • Explore the derivation of magnetic moments for various current configurations.
  • Learn about the implications of line integrals in physics, particularly in magnetic fields.
  • Investigate common notation errors in physics and their impact on calculations.
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Physics students, electrical engineers, and anyone involved in the study of electromagnetism and magnetic fields will benefit from this discussion.

ognik
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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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