Calculating magnetic field of finite solenoid

[bsully]

Hey guys! New guy here so bear with me on my first post:)

I'm trying to calculate the B field in the center of a finite solenoid for different outer radius sizes. I was able to find a formula online that gave the B field in the center of a solenoid given its length, inner radius, outer radius, number of loops, and current.


(sorry guys but I can't include links until I reach 10 posts - add "www" to each link)
Formula: .netdenizen.com/emagnet/solenoids/solenoidonaxis.htm


Using matlab, I plotted a graph of the B field with the outer radius as the input variable and all other variables constant. Here's the graph I created:

L = 0.0254m
Inner Radius = 0.008m
I = 100A
N = 100
Outer Radius varies from 0.008m to 1 m

IMAGE: .image-share.com/ijpg-1492-27.htm

Shouldn't the B field increase with increasing outer radius due to there being more turns per unit length?

 

[tiny-tim]

welcome to pf!

hey bsully! welcome to pf!

L = 0.0254m
Inner Radius = 0.008m
I = 100A
N = 100
Outer Radius varies from 0.008m to 1 m
…
Shouldn't the B field increase with increasing outer radius due to there being more turns per unit length?

no, the turns per length (the pitch) is N/L, which is constant

(btw, i couldn't see anything at http://www.image-share.com/ijpg-1492-27.htm )

 

[bsully]

Well now I'm embarrassed... I blame it on my lack of sleep:)

So based on what I have so far, I've found the B field for a solenoid with increasing outer radius but with a constant number of turns - i.e. the wire diameter is increased to maintain dimension.

I guess what I was trying to do was to keep the wire diameter constant - thus number of turns won't be constant. For example, find the B field inside a solenoid as I add layers of the same diameter wire(solenoid length, inner radius, and current kept constant). I figured this would be a way to decide at what point adding another layer of wiring to a solenoid would be useless as it wouldn't contribute much to the central B field.

 

[bsully]

finally figured it out.. replace N(number of turns) in the formula with N = (L/Dia)*((RO-RI)/Dia) where L = length of solenoid, RO = outer radius, RI = inner radius, and Dia = the diameter of the wire you are using.

Plugging into the formula:
L = 0.0254m (1 inch)
RI = 0.005m (5mm)
Dia = 0.001m (1mm)
I = 30Amps

0.005m < RO < 0.05m

i49.tinypic.com/1fxyzc.jpg (add 'http://' at the beginning - hope this works)

 

[alphysicist]

Hello and welcome to the forum! It's great to see someone exploring the topic of magnetic fields in solenoids. Your question about the B field increasing with increasing outer radius is a valid one. The formula you found online is correct, and it takes into account all the necessary variables to calculate the B field in the center of a finite solenoid. However, it is important to note that the B field is not solely dependent on the number of turns per unit length, but also on the radius of the solenoid.

As the outer radius increases, the overall size of the solenoid also increases, resulting in a larger volume for the magnetic field to spread out. This means that even though there are more turns per unit length, the B field may not necessarily increase at the same rate as the outer radius. In fact, there may be a point where increasing the outer radius further will have a minimal effect on the B field.

To fully understand the relationship between the B field and the outer radius, it may be helpful to plot the B field as a function of both the outer radius and the number of turns per unit length. This will give you a better understanding of how these variables interact to affect the B field.

Keep up the good work in exploring the world of magnetism and solenoids!