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How to correctly calculate coil's field strength?

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Trying to give you a simple answer based on analytical arguments (formula), I realized that the expressions given above do not refer to any arbitrary point within the circle other than the center. The expression for any point however is not simple, as can be seen here: View attachment Bfield.rar, it requires calculation by numerical integration, so I insist that you consider performing experiments with the aid of simulation tools for field solving.
 

andre_teprom said:
Trying to give you a simple answer based on analytical arguments (formula), I realized that the expressions given above do not refer to any arbitrary point within the circle other than the center. The expression for any point however is not simple, as can be seen here View attachment 154018, it requires calculation by numerical integration, so I insist that you consider performing experiments with the aid of simulation tools for field solving.
Click to expand...

Center is all i am asking about, that is, within the 4cm central gap.
 

FvM would please make another simulation.

This time coil is 16cm wide x 2.4cm heigh with 4cm central gap.

It has 450 turns and let's say current is 50A.
 

Are you now saying field is weakest at the center of the solenoid. I assume you mean since it is the farthest point from the coils looking inward. Or is there something I'm missing.
Click to expand...
Yes, weakest on the center line. In so far the field calculation over the full operation volume can be bypassed if you are only interested on the minimal field strength.

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Field becomes rather uniform, but maximum Bz is only about 0.2T due to the long coil. Total NI = 450*50

fieldpicture2.PNG

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The previous coil had only 120 mm length. One more with 160 mm, same NI. Bz, max reduces to 0.16T

fieldpicture3.PNG
 

FvM said:
Yes, weakest on the center line. In so far the field calculation over the full operation volume can be bypassed if you are only interested on the minimal field strength.

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Field becomes rather uniform, but maximum Bz is only about 0.2T due to the long coil. Total NI = 450*50

View attachment 154021

- - - Updated - - -

The previous coil had only 120 mm length. One more with 160 mm, same NI. Bz, max reduces to 0.16T

View attachment 154022
Click to expand...

What if we bring the height back down.

Now it's 28cm wide, 0.8cm high, turns are down to 300, same amps.
 

Although the coil dimensions are not fulfilling the "long solenoid" criterion length > 100*radius, the respective field strength value B = µ*NI/L can be used as a first estimation. Check with last two examples. Making the coil longer gets you closer to the long coil estimation. It gives 0.067 for NI=15000, L=0.28m
 

FvM said:
Although the coil dimensions are not fulfilling the "long solenoid" criterion length > 100*radius, the respective field strength value B = µ*NI/L can be used as a first estimation. Check with last two examples. Making the coil longer gets you closer to the long coil estimation. It gives 0.067 for NI=15000, L=0.28m
Click to expand...

Are you saying field in the center is only ~0.067T like this??
 

Yes, reduced NI + increased coil length compared to previous case. With sufficient coil length, the coil diameter doesn't affect the field strength.
 

FvM said:
Yes, reduced NI + increased coil length compared to previous case. With sufficient coil length, the coil diameter doesn't affect the field strength.
Click to expand...

How do you mean "increased coil length compared to previous case", length is decreased from 2.4cm to 0.8cm. I guess you mean diameter.

So, according to your simulation software there is no configuration with these parameters that can top 0.2T.

Or is there. Can we at least get to 0.3T with another combo?

For example...

Diameter 20cm, height 1.6cm, 400 turns, same amps.
 
Last edited:

Sorry, I see that I misunderstood your coil dimension specs. "Width" means diameter and "Height" coil length?

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Here you go with D=160 mm, L=24mm, NI=22500. Bz in the center is 0.3T.

d160_l24_ni22500.PNG

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The coils with larger diameter achieve lower field strength. Use a geometry where the average distance of windings to coil center point is minimal.
 
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    nix85

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Within your constraints you should consider a small diameter (5cm) Helmholtz coil configuration augmented with some neodymium magnets (N52 or better) placed along the axis. Or with an additional closed loop iron core solenoid with a commensurate air gap aligned with the helmholtz structure.

Otherwise one or another of your contraints will trip you up - wire dia, max current, heat dissipation, power supply capability etc etc.

Without your imposed constraints it is easy to make a uniform >=4 Tesla magnetic field.
 

FvM said:
Sorry, I see that I misunderstood your coil dimension specs. "Width" means diameter and "Height" coil length?
Click to expand...

Yes!

Here you go with D=160 mm, L=24mm, NI=22500. Bz in the center is 0.3T.

View attachment 154036
Click to expand...

Nice.

The coils with larger diameter achieve lower field strength. Use a geometry where the average distance of windings to coil center point is minimal.
Click to expand...

Whould you please try the last config i asked.

Diameter 20cm, height 1.6cm, 400 turns, same amps.

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kripacharya said:
Within your constraints you should consider a small diameter (5cm) Helmholtz coil configuration augmented with some neodymium magnets (N52 or better) placed along the axis. Or with an additional closed loop iron core solenoid with a commensurate air gap aligned with the helmholtz structure.

Otherwise one or another of your contraints will trip you up - wire dia, max current, heat dissipation, power supply capability etc etc.

Without your imposed constraints it is easy to make a uniform >=4 Tesla magnetic field.
Click to expand...

Yes, but those are not an option for what i'm doing.

As for heat problem you refer to, this is for short duty cycle pulses, not continous.
 

Whould you please try the last config i asked.

Diameter 20cm, height 1.6cm, 400 turns, same amps.
Click to expand...
I already did, as reported the center point field strength is lower, only 0.244 T. Thus I thought the simulation details are not so interesting.

d200_l16_ni20000.PNG
 

FvM said:
I already did, as reported the center point field strength is lower, only 0.244 T. Thus I thought the simulation details are not so interesting.

View attachment 154054
Click to expand...

Oh ok, tnx. I don't wanna bother you, but just once more please.

What is the field for diameter 13.6cm, height 3.6cm, 540 turns, same amps.
 

FvM said:
An older version of QuickField
Click to expand...

Last days i been in vain trying to find a company that would sell copper or aluminum flat wire in smaller amount, i contacted every company on Alibaba, Indiamart, few rare companies that make such wires in Europe, NO ONE wants to deal with small buyers. So i decided to go with round wire for now altho bit less efficient due to airgaps.

Anyway, i came up with new dimensions, would you please make another simulation.

Now i use 1.4mm round copper wire, 100m of it which is 1.1Ohm.

Dimensions 110mm x 23.8mm 425 turns, same current, same gap in the center of 4cm.

I downloaded Qucikfield but yet have to learn it.
 

So when you write 'same current' do you mean 50 amps?

And when you say it is 'pulsed', what duty cycle & frequency do you mean?
 

kripacharya said:
So when you write 'same current' do you mean 50 amps?

And when you say it is 'pulsed', what duty cycle & frequency do you mean?
Click to expand...

Yes, 50 amps. It's assumed we are talking DC,
duty cycle and frequency (and thus power) are totally irrelevant in the context.
I am looking for flux density, will it be on for a 10% or 100% of the time is another thing.
 

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