Field of a circular loop around its axis issue

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Homework Help Overview

The discussion revolves around deriving the formula for the magnetic field of a circular loop around its axis, focusing on the geometric relationships involved in the setup.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster questions why the differential length element (dl) is considered perpendicular to the vector (r) in the context of the circular loop's magnetic field.
  • Participants suggest visualizing the problem with a 3D model to clarify the geometric relationships.
  • There is an exploration of the orientation of dl and r in relation to the plane of the circle.

Discussion Status

The discussion has progressed with participants providing helpful visualizations and clarifications regarding the geometric setup. The original poster expresses understanding after the explanations.

Contextual Notes

Participants are working within the constraints of deriving a formula, focusing on the relationships between the elements involved without providing a complete solution.

Amaelle
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Good , i want to derive the formula for field of a circular loop around its axis
Magnetic+Field+due+to+a+Circular+Loop+carrying+current_.jpg

but i was stucked with the following point:
they consider dl perpendicular to r ! why is that??
many thanks in advance!
 

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It might help to construct a 3D model. Draw a circle on a piece of paper. Let the paper rest on a horizontal surface. Hold a pencil vertically with one end at the center of the circle. The pencil represents the axis of the circle. Choose an arbitrary point C on the circle and hold another pencil such that one end is at C and the other end touches the axis of the circle. This pencil represents r. Imagine a little element dl of the circle at point C. Can you see that r is perpendicular to dl?
 
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Because dl is perpendicular to the page (either coming out of the page or going into it), and r is in the page.
 
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thanks a lot both of you, now i can see :)
 

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