Field of a circular loop around its axis issue

In summary, during a discussion about deriving the formula for the field of a circular loop, it was mentioned that dl is considered perpendicular to r. One person suggested using a 3D model with a circle and two pencils to better understand this concept. It was explained that dl is perpendicular to the page and r is in the page, which helps to visualize their relationship.
  • #1
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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  • #2
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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Likes Amaelle
  • #3
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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Likes Amaelle
  • #4
thanks a lot both of you, now i can see :)
 

1. What is the field of a circular loop around its axis?

The field of a circular loop around its axis is the magnetic field that is produced by a current flowing through the loop. It forms a pattern of concentric circles around the axis of the loop.

2. How is the direction of the field determined?

The direction of the field is determined by the right-hand rule. If you point your thumb in the direction of the current flow, then your fingers will wrap around the loop in the direction of the magnetic field.

3. Does the size of the loop affect the strength of the field?

Yes, the size of the loop does affect the strength of the field. The larger the loop, the stronger the magnetic field will be. This is because a larger loop can accommodate more current, resulting in a stronger magnetic field.

4. How does the field change when the loop is tilted?

When the loop is tilted, the field lines become elliptical instead of circular. The strength of the field also decreases as the loop is tilted away from the perpendicular position. This is because the current is not flowing perpendicularly to the loop, reducing the overall strength of the field.

5. Can the field of a circular loop be used for any practical applications?

Yes, the field of a circular loop has several practical applications. It is commonly used in electromagnets, electric motors, and generators. It is also used in medical imaging machines such as MRI scanners and particle accelerators in scientific experiments.

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