Biot-Savart non-textbook Equation -- B at point above a loop but off-axis

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Discussion Overview

The discussion centers on calculating the magnetic field (B) at a point above a closed loop of current, specifically when that point is not at the center of the loop. Participants explore the complexities of this calculation and the behavior of the magnetic field in this scenario.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the lack of straightforward calculations for B at points above a closed loop that are not at the center.
  • Another participant references a previous thread but questions whether the examples provided only apply to points along the central axis of the loop.
  • A participant shares a graph depicting the magnetic field around a wire loop, indicating that the steepness of the transition in the field is influenced by the offset from the plane of the coil.
  • One participant expresses confusion regarding the interpretation of the graph, questioning the behavior of the magnetic field as they move across the loop.
  • Clarification is provided that the graph represents the vertical component of the field, noting that the vertical field inside the loop is opposite to that outside the loop.
  • A participant asks about calculating the total magnetic field strength over a path, considering whether to sum components or use vector operations.
  • Another participant suggests that the total magnetic field can be computed as the vector sum of the horizontal and vertical components.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and interpretation of the magnetic field behavior, with some confusion remaining about the graph and the calculations involved. No consensus is reached on a simple calculation method for B at off-axis points above the loop.

Contextual Notes

Participants note the complexity of the magnetic field's behavior and the need for clarity on the components involved in the calculations. There are unresolved questions regarding the graphical representation and the mathematical approach to summing the field components.

tim9000
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I read everywhere about the formulas for calculating B at a point from a length of straight wire, or at a point from the centre of a closed loop.
But what about at a point over a closed loop that wasn't the centre? Is there a simple calculation for that?

Thanks
 
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Thanks for the reply zoki, I only had a quick look, but didn't those examples still only deal with a point still being on the center (z) axis of the loop? (not like directly over the loop or closer to one side than the other)
I'll have a better look later, in which case if I'm wrong I'll remove this post.
Cheers
 
Attached is a plot of the field of a loop. This graph shows the magnetic field you would expect to measure as you walk across a wire loop resting on the ground surface. The loop is shown as the circle, viewed from above, modeled with many short segments as shown. The horizontal scale is in radii.
The plot drawn across the graph is the field that is seen traveling along a line that passes through the axis, parallel to, but slightly away from the plane of the loop. The plot is normalised so that +Bo is the axial field value.
The steepness of the transition while crossing the wire is determined by the offset from the plane of the coil. Let me know if you find an analytic solution.
B_Field Circular _Loop .png
 
I'm not sure I get it completely (cool graph by the way), I'm really sorry.
So there is a wire loop of current on the ground, I'm walking above it from -2 to +2, passing through the center of the axis of symmetry. I don't see how the yellow graph can be B? All I can picture is current traveling, say, anti-clockwise, then I would have through if the yellow graph was B, that as I approach it and am at -1 it peaks and all the B is coming from the LHS then as I am at the middle, the only component is from the center and there is some cancellation diagonally, then as I leave a gain at 1 it peaks with just RHS magnetic field. So why would it go negative as I first approach it, and leave why would it have a negative gradient? I would have thought it would taper up as I approach, peak, taper down (due to cancellation), taper up, peak, taper down.

Thanks heaps!
 
So I thought it would look like this:
looklike.png
 
Sorry, the graph is the vertical component of the field.

The vertical field inside the loop is opposite that outside the loop.

Over the wire the B field is horizontal so it has no vertical component.
 
Ok that makes sense, but what if you wanted the total B strength, not just a component, over the path from left to right?
Would you sum the components, dot product, or cross product?
Cheers
 
You would compute Bhorizontal and Bvertical, the total is the vector sum, B = √(Bh2 + Bv 2)
 
  • #10
Ah of course,
Thank you very much
 

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