Confused about solenoid radius from this site

[ZecronTech]

So I was reading a thread on PF talking about the radius of a solenoid and Bob S answered with a link:

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.

 

[mfb]

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.

 

[ZecronTech]

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.

 

[mfb]

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.

 

[ZecronTech]

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.