Confused about solenoid radius from this site

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Discussion Overview

The discussion revolves around the radius of a solenoid and its impact on the magnetic field, as referenced from a specific website. Participants explore the implications of the equation provided on the site, particularly in relation to the number of coil layers and their respective radii.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant expresses confusion regarding the equation for the radius of a solenoid, questioning how a single layer of coil with equal inner and outer radii could produce a larger magnetic field than multiple layers where the outer radius exceeds the inner radius.
  • Another participant seeks clarification on where the equation states that the radius equals the outer radius minus the inner radius, suggesting that the finite width of the cables must be considered.
  • A participant assumes that increasing the number of coil layers would lead to a greater difference between the outer and inner radii, resulting in a weaker magnetic field, which they find counterintuitive.
  • One participant cautions that the radii are involved in logarithmic calculations, indicating that the overall effect on the magnetic field strength is not straightforward without further calculations.
  • A later reply acknowledges a mistake in their reasoning, indicating a realization about the logarithmic relationship and its implications for the magnetic field strength.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between the number of coils, the radii, and the resulting magnetic field strength. There is no consensus on how these factors interact, and the discussion remains unresolved.

Contextual Notes

Participants note the complexity of the equations involved and the need for calculations to determine the dominant effects of the variables discussed.

ZecronTech
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So I was reading a thread on PF talking about the radius of a solenoid and Bob S answered with a link:
Bob S said:
This equation for the on-axis field is exact both inside and outside the solenoid:

http://www.netdenizen.com/emagnettest/solenoids/?solenoid

You can add more layers at the ends.

Bob S

On that site, it states that the Radius = the outer radius - the inner. It doesn't make sense. What happens when there is only one layer of coil and the outer radius (OR) is basically the inner radius (IR). That would create a larger magnetic field than if I had multiple layers of coils and the OR > IR which would then create a smaller one. I don't understand why.
 
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On that site, it states that the Radius = the outer radius - the inner.
Where?
What happens when there is only one layer of coil and the outer radius (OR) is basically the inner radius (IR).
Even in that case, your cables have a finite width.

You can probably consider this equation in the limit r1 -> r2, and get a simpler equation for the case where the difference between both is not significant.
 
mfb said:
Where?

In the equation where the denominator is 2(r2-r1). So I'm assuming that the more layers of coils you have, the greater r2-r1 is and therefore less magnetic fields. Which I don't get. I thought the more coils you have, the greater the magnetic field.
 
Careful, the radii are used in the logarithms as well. It is not clear which effect will dominate if you don't calculate it.

"More coils" would also increase n (more windings) or I (more current), cancelling this effect. More coils give a higher field strength.
 
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mfb said:
Careful, the radii are used in the logarithms as well. It is not clear which effect will dominate if you don't calculate it.

Oh...Whoops. Thank you. I can't believe I forgot about that.
 

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