Question on air cored coils and field strength at a distance X from the center of a coil diameter D.
Does the field strength depend much on D when X>>D?
-- Dirk
Sure, it does. D=3D 0 pretty much kills the field at all distances.
Well, lets plug in some numbers. N turns, distance 200cm, D = 5cm dia, D = 20cm dia
-- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.blogtalkradio.com/onetribe - Occult Talk Show
e
org/- A UK political party
Same current through the coil in each case? Since the field at a distance is the vector sum of the contributions for each increment of distance along the wire carrying the current, consider the easy case of measuring the field at 200cm (or whatever) along the axis of the helix that is the coil. To make it VERY easy, consider just a single turn, say in the X-Y plane at Z =3D 0. Then to the approximation that the angle subtended by the turn from the measurement point (e.g. at Z=3D200cm) is zero, the field will be directly proportional to the length of wire in the turn, which is just proportional to the diameter of the turn. It should be apparent to you that there is a cosine term to account for the fact that the pieces of the turn are not all the same direction away from the measurement point.
It would not be a terrible problem to calculate the field accurately for any point at a distance from a helix carrying uniform current, no? If you can't do it analytically, certainly it would not be difficult to set it up to calculate numerically (using something like Scilab or even a spreadsheet).
Cheers, Tom
e
The dipole moment of a flat coil (ignore solenoid length) will be proportional to current times area
Mdipole =3D k *N * I * D**2
and the distant field of a dipole is of magnitude
Mdipole/R**3
(that's the far-field approximation, there are other moments that provide minor corrections).
So, the far-field is gonna be proportional to D squared.
Thanks to you and Tom Bruhns. So, for a fixed length of wire on both coils, with N obviously varying according to the diameter, we end up still proportional to D^2, but with a different constant of proportionality?
-- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.blogtalkradio.com/onetribe - Occult Talk Show
No, of course not. If the N value isn't independent of D, you have to recalculate that dipole moment with the N replaced by the correct function of D; 'fixed length of wire' is a new requirement, and changes the problem significantly.
N = L/(D*Pi) to a good approximation
-- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.blogtalkradio.com/onetribe - Occult Talk Show
org/- A UK political party
At large distances you can treat the coil as a dipole. The dipole moment goes as the number of turns, current and the area. (If I recall my freshman physics correctly.)
George H.
the
.Yup, that's it. You can look up all the details in any good physics text.
George H.
th
oorg/- A UK political party
Where did the L come from?
George
UK
Sorry - wrong L! I meant l = length
-- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.blogtalkradio.com/onetribe - Occult Talk Show
UK
So with a fixed length of wire there is a linear tradeoff between diameter and number of turns. Hence as the coil diameter increases the distant field increases linearly? Last time I did this physics was about
35 years ago!-- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.blogtalkradio.com/onetribe - Occult Talk Show
A UK political party
Hello Dirk,
Assuming X>>D and X>> length of coil.
H-Field at distance is proportional to A, 1/(X^3), N and current.
A = area occupied by the coil (for example 0.25*pi*D^2 for circular cross section) X = distance N = number of turns.
The constant multiplier for X perpendicular to the winding is 1/(2pi) (you look through the turns) The constant multiplier for X in the plane of the winding is 1/(4pi). The shape of A is not of importance
The product I*N*A is called "magnetic moment" (I=current).
When you take a rectangular cross section, assume X>>D, and use the Biot-Savart formula, you can derive the formula without lots of math.
Note that formula can only be used when observation distance X
e
.org/-A UK political party
org/- A UK political party
Dirk, A fixed length of wire is a differernt problem... But we can use calculus to get the answer. (My guess is that you get the biggest field with a single turn.) OK forget the calculus, it's pretty easy to see that going from one turn to two turns reduces the dipole moment.
George H.
party
UK
The problem I have is that I have a fixed length of wire, and I want to find the best way of winding it to get the best field at a couple of meters. Obviously the absolute best is a coil 4m in diameter! I'm just wondering about the scaling factor, whether its linear or power law as the coil becomes smaller.
-- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.blogtalkradio.com/onetribe - Occult Talk Show
the
s.org/-AUK political party
ut
.org/-A UK political party
sy
org/- A UK political party
OK what's the length of wire and how far is the distance? (And what is the 'best' field? Do you mean highest field strength?)
George H.
party
UK
The length is around 80m, and I'm looking for highest field strength. The other constraint is packaging - obviously I cannot make a 4m dia coil, hence the original question.
-- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.blogtalkradio.com/onetribe - Occult Talk Show
To add a bit more info, I can probably go to around 30cm dia max. I want to know (say) how this compares to a coil 10cm dia. If the field strength tradeoff is linear it might be acceptable.
-- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.blogtalkradio.com/onetribe - Occult Talk Show
nsu...
ow
le
the
se
easy
to
t sorg/- A UK political party
Hello Dirk,
Yes, with a given wire length, the H-field (or B-field) at large distance is proportional to D.
I don't know the current through the coil, but when it is significant and AC, you might run into thermal issues. Due to proximity effect, the AC resistance can be significantly higher then based on a simple skin depth calculation.
Best regards,
Wim PA3DJS
ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.