Formula Spreadsheet
AC formulas
AC is frequenctial current. and can be ordered into 4 different triangles.
Each triangle respond to the Pythagoras formulas, with one hypothenus, and two kathets. The kathets form a 90 degree angle.
The Horiosontal kathet represent the Resistive or DC domain of the circuit (real).
The Vertical kathet represent the AC loss or reactive values (imaginary) .
The Hypothenus is however the "actual" value during AC operation.
In my own terminlolgy.
Triangle 1 : Hypothnus = U = Volts, Horizontal kathet = U_R Volt Resistive. Vertical kathet = U_X Volt Reactive
Triangle 2 : Hypothnus = I = ampere. Horizontal kathet = I_R Ampere Resistive. Vertical Kathet = I_X = Ampere Reactive
Traingle 3: Hypothenus = S = VA. Horizontal kathet = P = Watt "P for Power". Vertical kathet = Q = var Volt ampere reactive or "Q for Quality" in radioscience this is "damping" in the antenna or coax. In audio filtering it is the wide or narrow band of the frequency specter through the speaker, on the electric guitar this has a knob named "Tone", see Humbucker coils. On Digital Sequencers and EQ`s there is a button called Q, and this shapes the curve wide or narrow, allowing just a selected frequenctial band pass through the speakers. This is also the factor that can be tuning the coil into electrical resonance or an "electrical echo" between the terminal ends, by adjusting the capacitor. I would interpret a large value of Q= var as a Low damping, allowing most of the various frequencies from the generator or musical instrument pass. whereas a coil with Low Q= var has a high damping, meaning the coil allows passage for just a narrow band of frequencies ( it might be the other way around ). The Q = var in the AC formula is not the same as Q= coloumbs in the capacitor. Q (coloumbs ampere second) = C (farads) * U (volt) . it seems, but they also seem related, needs more investigation.
Triangle 4 : Hypothenus = Z Impedance, resistance with frequency. Horizontal kathet = R Ohm Resistive. Temprature losses are in the Resistive domain. Vertical Kathet = X Reactance, A collecion of losses in self induction and core hysteresis (remagnetisation of the Iron, due to magnetic saturation . The electrons cant keep up the frequenctial shifts from North to South, and lag in the middle of the Iron material, and cancels eachothers polarisations out). In other words, the Facoult (Eddy) currents are counter acting the magnetic polarisation in the Iron. Like a paddle in the water, can set up a small tornado or whirl in the water , resisting the paddle to move backwards agains the rotation of the swirl.
When a certain coil is constructed and tested. One can calulate the cosinus phi, and when drawing the 4 triangles, all the triangles shall share the same cosinus phi value and angles. It is for a reason that Pythagoras formulas may be the most useful formulas known to humanity, For it can be used in music and electrical inducstry as to coils and electric motors. See for instance the note A 440 Hz * SQRT2 = 440 * 1.41 = 622.2 Hertz. That is a D# in the 12 tet temprament system or 6 semitones up from note A. Playing the A and D# on the guitar or a keyboard practically plays a Likesided triangle, that is bothe the Kathet "string A" and Hypothenus "string D#". It doesnt produce a beautiful harmony and was back in the days bamnned by the Christians this particular chord, for mystical reasons !Pythagoras is also credited with the phrase " Numbers is the origin of Gods and Demons". In my philosophy a God is a harmonic realtionship, and a demon is a disharmonic relationship. The word "Arch" would be handed over to the readers imagination to conceptualize. Whether Pytagoras was a person from Hellas or a group of people, belonging to a school of mathematics, most certainly inherited much of their teachings from Farao in Egypt, it may be the concepts of PTH tha Egyptian God of engeneering, however it remains uncertain. The spelling of their names is very similar Ptha and Pythagoras.The AC generator is practically a musical instrument, and often called a "Tone Generator" or "Harmonic Generator".
These are the formulas I have obtained.
From cross calculating the values from the schoolbook or ground book of basic electricity and my own measures. In the chapter of "the electric grid", or maybe "installations for light control"." effect vector diagrams", phase compensation.
Keep in mind that most of these values are obtained only after the model is built. the Volts and Resistance may be the only "safe" values from a desktop perspective, that is the socket or supply voltage, and the ohm per meter on the wire crossection. Keep in mind that as the temprature increase of the wire the resistance also increase, so Resistance is only a constant as long as the temprature is constant. The temprature loss that is understood as a Blackbody radiation, the heat loss can actually be translated into IR or infra red loss ! Infra red is a "electromagnetic" ( or radiant ) waveform that transmits heat with the speed of light, but the wavecompression over a distance of vacuum isnt in itself hot. its heating action only applies when a molecule or atom is being struck. I think the IR adds vibration to the atoms or molecules, and the friction between them transmit a heat wave that is again sensed by the nerves in the fingers or the environment. I think that the IR wave is generated by the nucleus, and not the electrons, for It would not be impossible that a static object, or an object stripped of electrons become hot. It can be argued that the Amperes that are electrons that travel over a wire creates heat, and that is true in my opinion. But I counter that argument by claiming that its the atoms that are being stirred by the electric motion and this way the atoms in the copper wire vibrate until their solid bonding turn fluid. Aother argumetn is how can a DC current generate a Infra red alternating waveform in the gigahertz range, that is low frequency light waves or heat ? Yet another interesting thing with heat is that almost all materials generate the same waveform in the heat spectrum. Temprature is also very unlike a magnetic field, for a cup of hot water can be turned upside down to become cold ! like a opposite polarity of a magnet. sharing some characteristics with the uncoprehensible complexity of gravity. Gravity atracts everything, and doesnt repell any material, One can turn an object sideways or upside down, there is no change in the gravity field, only the number of particles determine the gravity, in my understanding . a statemmetn may be that soem fields have polarity and others have not. the static and magnetic fields have polarities, Temprature and Gravity does not have polarities.
Its still quite a challenge ( If possible at all) to calculate the cosinus phi or the Reactive values of a Secondary coil with just knowing the Ampere and Resistance, without knowing the Volts of the secondary. For that I need a Voltage Divider, to reduce the voltage so the digital Volt meter wont be destroyed . The cosinus phi depend on the coiling geometry, frequency, self induction and the capacitance. A certain man named Nikola Tesla whose excellence remain hidden deep in the future, managed to make his coils with the proper capacitance in the coil itself, not needing an external capacitor ! Different coiling geometries might be a long and narrow coil (solenoid) or short and wide (spiral coil), Or more usual a coil with several layers of wire.
Ampere
I = U / Z = S / U = Q / U_X = P / U_R = I_R / cos phi = I_X / sin phi = SQRT Q/X = SQRT S/Z = SQRT P / R = P / (U * cos phi) = Ampere
I_X = U_X / Z = Q / U = sin phi * I = SQRT I^2- I_R^2 = Ampere Reactive
I_R = U_R / Z = P / U = cos phi * I = SQRT I^2 - I_X^2 = ampere Resistive
Volt
U = P / I_R = Q/ I_X = S / I = U_R / cos phi = U_X / sin phi = U_R^2+U_X^2 = I * Z = I *R / cos phi= Volt
U_X = Q / I = Z * I_X = X * I = U * sin phi = SQRT U^2 -U_R^2 = Volt Reactive
U_R = P / I = Z * I_R = R * I = U * cos phi = SQRt U^2 - U_X^2 = Volt Resistive
Watt (Effect)
S = P / cos phi = U * I = Z * I^2 = SQRT P^2+Q^2 = U^2 / Z = VA (Volt Ampere)
Q = U * I * sin phi = U * I_X = X * I^2 = U_X * I = sin phi * S = SQRT S^2 -P^2 = var
P = U * I * cos phi = U * I_R = R * I^2 = U_R * I = cos phi * S = SQRT S^2 - Q^2 = U_R^2 / R = Watt
Resistance
Z = U_R / I_R = U / I = R / cos phi = X / sin phi = SQRT X^2 + R^2 = S/I^2 = U^2 / S = Z ohm, impedance, (Resistance with frequency)
X = U_X / I = sin phi * Z = SQRT Z^2 -R^2= Q / I^2 = (U_X^2 / Q...?) = X Ohm Reactance
R = U_R / I = cos phi * Z = SQRT Z^2-X^2 = U_R^2 / P = P / I^2 = R Ohm Resistance
Power Factor
cos phi = P / S = R / Z = I_R / I = U_R / U = tan^-1 (I_X / I_R)
sin phi = Q / S = X / Z = I_X / I = U_X/ U
Angle Degrees
Cos phi = cos^-1 (P/S) = sin^-1 (Q/S)
sin phi = cos-^1 ( Q/S) = cos ^-1 (P/S)
Approximations of Z impedance
Z = (U/I from DC) / cos phi estimate = R / cos phi estimate
Approximation of I ampere
I = (P/U from DC) / cos phi estimate
The following formula for henry is rearranged from a capacitor / coil phase compensation formula in the common science (my electrical groundbook) , known as
X ohm = 2 * pi * hz
by dividing both sides of the = sign with 2 * Pi * hertz one results in this :
X ohm / ( 2 * pi * hz) = 2 * pi * hz * L / (2 * pi * hertz)
the similar values are stroked out from the equation and the result will be as follows.
X ohm / 2 * pi * hz = L / 1
L = X ohm / 2 * pi * hz = henry
Id be happy to get a comment on that, for I do not know exacly what that number or value means ...
Likewise the Cap can be calculated like this
X ohm = 1 / 2 * pi * hz * C ( farads)
multiply both sides of the = sign with 2* pi * hz and get
X ohm * ( 2 pi * hz ) / 1 = 1 * ( 2 * pi * hz ) / 2 * pi * hz * C
1 / C = 2 * pi * hz * X ohm
One can flip it around once more and get
C farad = 1 / 2 * pi * hz * X ohm
Phase Compensation :
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14.08.2016
Magnetic Field Strenght
Interpreting the formulas is a study in itself. and concerning the H = A/m. Noted as Magnetic field strenght.
H = magnetic field strenght measured in Ampere per meter. ( seemingly not H = henry... !)
A/m = Depending on the formula. The value is a 1 dimensional line either in the center of the core, measured in meter between the first and the last turn. Or the Ampere per diameter of the wire, or the Ampere per Circumference of the wire.
This formula express the Ampere Turns per Meter as one value for "magnetic field strenght".
H (coil center axis) = I ( Ampere ) * n turns / l lenght in meter = A/m ( a central line in the coil core )
This formula does not concerne the diameter of the coil, and has no value for width; that must be calculated using another formula. In my interpretation of this formula, since there is no diameter, The coil is wound on a hair thin core, And after some thought the radius or diameter of the cylinder may not play any difference in this formula. the radius determines the circumference of the coil and thus relates to the resistance of the wire on the coil. Even tho the drawings accompanying the formula usually render a nice and large coil, the formula is rather illusive, if not unusable ! neither does it concerne the crossection and the temprature of the coil.
1st attempt (abandoned go to 3rd attempt )
I just discovered a method to transform a multi layered coil into a Solenoid. Lets say I have a coil that is 10 turns tall * 10 layers thick, conveying 2 Amperes in the wire. the Ampere Turns will be :
Coil Ampere Turns = 10 turns * 10 layers * 2 A = 200AT
Now I divide away the layers, making it a 1 layer coil, then multiply the ampere by the division factor. the factor is the number of layers
10 layers / 10 factor = 1 layer
2 ampere * 10 factor = 20 Ampere
Solenoid Ampere Turns = 10 turns tall 1 layer thick * 20 Ampere = 200AT
Lets say the coil is 5 cm tall
l ( lenght in meter) = 5 cm = 5 * 10^- 2 = 5E-2 = 0.05 meter
H (coil center axis) = I * n ( turns) / l (lenght meter) = 20A * 10 turns tall / 5cm E-2 = 200 / 0.05meter = 4000 A/m
This is the same as
H (coil center axis) = I * total turns / l = 2A * 10 turns * 10 layers / 5 cm E-2 = 200 / 0.05meter = 4000 A/m
so the conversion from a multi layered coil to a solenoid is actually not neccesarry.
2nd attempt ( abandoned . go to 3rd attempt)
In my quest for understanding the formulas another interpretation has presented itself. It deviates slightly from the conventional formula but use them as construction basis. And I have come to form 3 formulas, one for the solenoid, and multilayered coil that is longer than it is wide : N Turns > N Layers. One formula for when the coil is squared or block coil : N Turns = N Layers , and another when the coil closes into a spiral coil : N Turns < N Layers. In my mind the coils magnetic field must be weaker the longer it is, but equally weaker the wider it is if its a spiral.
Lets say I have a coil of 900 turns, carrying 2 amperes. the wire diameter is 1mm
I = 2A
Wire Ø diameter = 1 /1000 = 0.001 meter
900 turns in meter = 900 turns * 0.001 meter = 0.9 meter long coil
30 turns in meter = 30 turns * 0.001 meter = 0.03 meter long (or tall)
1 turn = 1 turn * 0.001meter = 0.001 meter long
conventional formula
H = I * N turns / lenght meter
H = 2A * 900 turns / 0.9 meter = 2000A/m
What if I want to have 2 layers and half the lenght ?
I came up with this formula
Solenoid single layer
H (turns > layers) = (I * N turns * N Layers) / (coil lenght meter / coil width meter)
H = 2A * 900 turns * 1 layer / (0.9m long / 0.001m wide) = 1800AT (ampereturns) / 900=
H = 1800 AT / 900 = 2 A/m
This value is significantly lower than the conventional number ! but then again consider this coil is 90 cm long ! ( (90 cm /30.48 = 2.9 imperial feet) . and 1 layer thick. Or expressed more figuratively, the diameter of the wire is the radius of the coil, making the coil 2 mm in diameter. There is NO chance the turn on the far end can have any magnetising effect near the projection pole on the other side. thee donut hole or cylinder core or pole projection is a name I am now calling "Projection face". It also seems to me that the donut hole of the coil has the strongest magnetic field concentration. and the magnetising target, usually Iron, should match the diameter of the coil core, or projection face, not the entire coil with the windings, just the hole in the middle. that statement is based on when I have a coil with amperes in it. The iron filings are mostly attracted to the inside of the coil, It may be the circumference of the outer turns are greater, making the filed lines tight at the inner turns. I want to add that I measured about 320Ampere Turns to lift 1 gram of sheet iron ! and it seemed the more close the iron was shaped the inner hole diameter the better the attraction became. And I need about 30Ampere turns to get a feeble response in iron filings at the center of a 1 cm diameter coil, the 30AT thus creates a magnetnic response to iron filings at about 5 mm or so. Leading to a formulation that if I have another coil of the same measure, more than 0.5 cm away , the magnetic field wont add to the former, so distance of the turns makes a big differance. The coil above calculated has neither has a radius or a diameter. so its basically a wire coiled on a core less than a hair thick.
Solenoid ( 2 layers ) multilayered
Turns = 900 / 2 = 450 turns
layers = 1 * 2 = 2 layers
Lets say I want to half the lenght and instead have 2 layers.
H (turns > layers) = (I * N turns * N Layers) / (coil lenght meter / coil width meter)
H = (2A * 450 turns * 2 layers ) / (450 turns * 0.001meter / 2layers * 0.001meter ) =
H = 1800 AT / (0.45 / 0.002) = 1800 AT / 225 = 8 A/m
By making the coil shorter and increasing the layers the A/m increases too, while the number of turns are kept the same. As expected.
Now the block coil or Squared coil where the Turns long is equal to the number of layers
Block (squared) coil ( N turns = N Layers)
turns = SQRT 900 = 30 turns long
Layers = SQRT 900 = 30 layers wide
H (turns = layers) = (I * N turns * N Layers) / (coil lenght meter / coil width meter)
H = (2A * 30turns * 30 layers) / (30turns * 0.001 / 30layers * 0.001 )
H = 1800 AT / 1 = 1800 A/m
Here one can see that the number under the fraction line becomes 1. and that is the largest number that can appear in the formula. so the block or squared coil has the maximal A/m for a given coil geometry.
then lets increase the layers even more and approach a spiral coil. In my understanding the A/m cant become more than the solenoid or the block coil, for all coils have an Ampere Turn of 1800 AT in this examples. the way I worked around it is to reverse the number beneath the fraction line once the turns are less than < the Layers.
spiral coil multilayered
Turns = SQRT 900 = 30
Layers = SQRT 900 = 30
And I want it to be double as thick as it is long, using a factor of 0.5
Turns = SQRT 900 * 0.5 = 15 turns long
Layers SQRT 900 / 0.5 = 60 layers wide
double check = 15 turns * 60 layers = 900 turns total
H (turns < layers) = (I * N turns * N Layers) / ( coil width meter / coil lenght meter /)
PS. Notice here that the width and lenghts are switched under the fraction line !
H = (2A * 15 turns * 60 layers) / (60 layers wide * 0.001m / 15turns long * 0.001m)
H = 1800AT / 0.06 / 0.015) = 1800AT / 4 = 450A/m
spiral coil
turns = 1
layers = 900
H (turns < layers) = (I * N turns * N Layers) / ( coil width meter / coil lenght meter /)
H = 2A * 1 turn * 900 layers ) / ( 900 layers wide * 0.001 / 1 turn long*0.001) =
H = 1800AT / (0.9m / 0.001m ) = 1800 AT / 900 = 2A/m
From this formulas a spiral coil of 900 turns wide, is equally poor in its Ampere per meter than a long solneoid of 1 layer and 900 turns ! To me it makes sense. Consider the actual size of the spiral coil above mentioned. its radius is 900 turns each turn is 1 mm making it a disk about 1.8 meters in diameter ( just under 6 feet in diameter) ! There is no chance the outer turn can magnetise all the way into the center turn with 2 amperes in the wire ! But it might be wrong. And I presume much better formulas can be devised. the problem is that it cant be used with conventional A/m values. but then again I have not seen any general formula concerning the multilayered coil ! the benefit of this approach is that it can be applied to both B = tesla, and L = henrys in the same way. When the A/m is determined, then one can move on to find the desired Projection face (projection pole), or opening of the donut hole, or diameter of the coil. to fit the generator pole or the target it is to magnetise. In so doing also determining the Resistance of the coil, and lenght of wire to spend.
Summary
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3rd attempt.
25.09.2016
I have chose to abandone the above formulas, named attempt 1 and attempt 2 . And replace them with the following below. In this 3rd attempt to understand the H = A/m, B = u0 * H= tesla and the L = henry. I have also chosen to rename the suffix in the H = A/m into H = Ampere Turns / per coil lenght in meter. I had a hard time understanding what actually is "Ampere per meter" . then suddenly I realised it had to be Ampere Turns per meter. but not per meter. but per coil lenght, measured in metric units. The formula of the "attempt 2" where I divided the Ampere * Turns / lenght * width gave a rediculus large value and cant be true. I then figured that a Solenoid of 1 layer had to be half the value of a 2 layered coil. I write it down here so I know where they are .
Spiral Displacement of Wire
If your really picky, and have a very long wire. As the wire is coiled around the core. Each turn as it is put beside the other, the lenght of each turn increases by 1 wire diameter, The turn lenght is equal to the circumference of the core pluss half the diameter of the wire pluss another diameter of the wire as the turns are put beside one another. When many wires are coiled this tiny amount of wire may accumulate some additional Ohms or resistance. I have developed a formula for N number of turns . A description to the formula. One loop turn of wire around a core in 3 dimensions, can be broken down or illustrated or rather modelled by having a piece of paper that is square, then draw a diagonal line with a pencil on that paper. Rolling a piece of paper into cylinder and a perfect Sinius is formed over the paper cylinder. If you havent done it before, its an act of magic ! The 2 dimensional Diagonal, is a 3 dimensional Sinius curve. Therefore a diagonal and the square format, can be used to determine the wavelenght ( or rather the lenght of the sinius shape...!), as well as turns of wires around a cylinder, And logically related to Square root of 2. Thus Pythagoras formula can be used. ( I have yet to figure out a proper formula for a spiral . That is very difficult to determine the lenght of a spiral wire .) this formula only applies for the first layer. I have managed to obtain a set of 5 formulas that needs to be used in succession as the layers progress. but its totally uneccesary.
X = lenght of 1 turn, or circumference of the core, pluss half a diameter if the first layer.
Y = total lenght of the core, lenght measured between the pole projection faces.
Z = total lenght of spiral wire
For 1 turn.
Z = SQRT X^2 + Y ^2
for 2 turns
Z = (SQRT X^2 + (Y/2)^2) * 2
for 8 turns
Z = (SQRT X^2 + (Y/8)^2) * 8
For any turns N turns
Z = (SQRT X^2 + (Y / N turns))^2 * N turns
Example
Core diameter = 3 cm
Core circumference = pi * 3 = 9.42 cm = X
Coil height = 10 cm = Y
N = 1000 turns
Z = SQRT X^2 + (Y/1000)^2 * 1000
Z = SQRT 9.42^2 + (10/1000)^2 * 1000
Z = (SQRT 88.82 + 0.0001) * 1000
Z = 9.42444 * 1000 = 9424 cm long wire ( then obtain the Ohm per meter.)
This version is abit shabby, for the wire diameter is not included. Needs an update that inkludes the wire gauge . You gonna calculate . or coil ?
Magnetic field strenght in the center of one winding.
In this formula one can "focus" the magnetic field from weak to strong by narrowing down the diameter of the coil. Making the poles more intense.
r (radius in meter) = 2.5cm = 2.5E-2
What this formual express is the Ampere / Diameter . for 2 * Radius = 1 Diameter
H (turn) = I / 2 pi * radius in meter
H (turn) = 2A / 2 * pi *2.5E-2 = 12.73 A/m ( Magnetic stenght over the diameter of the wire )
Version with the multilayered coil "transformed" into a solenoid.
H (layer ) = 20A / 2 * pi * 2.5E-2 = 127.3 A/m
Magnetic Field Strenght in a point outside a straight conductor
This formula Express Ampere per Circumference.
r = radial distance outside the conductor in meter, lets say 0.5 cm
H = I / 2 pi * r
H = I / pi * radius * 2
O circumference = Pi * Radius * 2
H (turn) = 2A / 2 * pi * 0.5cm E-2 = 0.0063A/m ( Magnetic strenght over a circumference around the conductor)
Add 10 turns from the multilayered coil
H (layer) = 20A / 2 pi * 0.5cm E-2 = 0.063 A/m
This is the same as multiplying in 10 more turns
H (layer ) = (2A / 2 * pi * 0.5cm E-2) * 10 turns = 0.0063 * 10 turns (spiral) = 0.063 A/m
Now presume that the multilayered coil is only having 1 turn and 1 layer, but the same volume of copper mass ! Just a block of copper coiled 1 turn around a core. that is a coil with no turn subdivisions. A bus bar in a loop.
The coil origionally has 10 turns * 10 layers = 100 turns * 2 Ampere = 200 AmpereTurns
Now divide away all the turns and layers and use the division number to multiply into the ampere.
100 turns / 100 = 1 turn coil
2A * 100 = 200A
H ( coil ) = 200A / 2 * pi * 0.5 E-2 = 6366 A/m at 0.5 cm distance from the coil windings, supposedly. Then you can ask yourself. what do I do with that number ?
Kirchoffs Parallell coppling
R = 1 / (1 / R1 + 1 / R2 + 1 / R3) = 1 / ( 3 / R_tot ) = ohm
R1 = 10 ohm
R2 = 20 ohm
R3 = 30 ohm
By having a parallell coppling one practically increase the crossection and the Ohm is reduced, compared to a series coppling that adds the resistance and is a natural adding value. The parallell is therefore a natural division . I see it as 2 terminal lines that are bridged with "pipes" of unequal thickness conveying water (Ampere) between the potential (Volt) .
Parallell Circuit
Terminal 1 Terminal 2
| |
| |
|.......10 ohm.......|
| |
|.......20 ohm.......|
| |
|......30 ohm........|
Find the common multiplum of the Ohms
10 = 2 * 5 -> * 2 * 3
20 = 2 * 2 * 5 -> * 3
30 = 2 * 3 * 5 -> * 2
Multiplum = 2 *2 * 5 * 3 = 60
Kirchoff parallell = 1 / (1*2*3 / 10 ohm* 2 * 3 + 1*3/ 20 ohm* 3 + 1*2/ 30 ohm * 20 ) = 1 / (6 /60 + 3/60 + 2/60 ) = 1 / (6+3+2 / 60 ) = 1 / (11 / 60) = 5.45 ohm
As far as I know the schoolbook and conventional formulas does not have the "1 / " (1 / R1 + 1/ R2). ontop, therefore making a confusion in the end result. the conventional formula suggest one has to flip the Numerator and denumerator of the fraction like this
Conventional Parallell = 1 / 10 ohm + 1 / 20 ohm + 1/ 30 ohm = 6 / 60 + 3 / 60 + 2 / 60 = 6 + 3 + 2 / 60 = 11 / 60 => magic flipover => 60 / 11 = 5.45 ohm. I just could not understand how on earth 11/ 60 = 60 / 11 ! and even worse it gives the correct answer to the measure . This is however solved by putting it like this 1 / (11 / 60 ) = 5.45 ohm . In my opinion that should be considered in the electrical teachings.I wouldconsider the coil as the most useful tool for what modern life concernes. And after a while of making coils, youll be counting turns in your sleep !
Planning out a coil
This is the way I do it usually. I start with knowing the supply voltage. Lets say a 12V or 230V source. Then I plan it using DC current, then apply the cosinus phi later on if its a AC coil. I have a number of steps I do.
1. Start by knowing the formula of the ideal transformation if its a transformer. A motor coil is practically also a transformer. Unless permanent magnets are used. the usefulness of this formula is to approximate the number of turns on the secondary coil, when considering a transformer, the unusefulness is that its ideal and not considering the temprature losses. losses over distance between the coils or reactance in the coils
k ( coiling constant) = U1 / U2 = N1 / N2 = I2 / I1
Transformer
U1 = Volt primary
U2 = Volt secondary
N1 = Turns Primary
N2 = Turns secondary
I1 = Ampere primary
I2 = Ampere secondary
To know the number of turns on the secondary. Lets say I want 10000V or 10kV on the secondary and have a 230V AC supply. how many turns on the secondary. In this case I must presume that the ampere in the primary is low enough not to overheat the coil. and large enough to encapsulate the entire secondary with a magnetic field. Lets assume that I have 1000 turns on the primary, N1 = 1000 turns.
k = U1 / U2 = 230V / 10 000V = 0.023
N2 = N1 / k = 230V / 0.023 = 1000 turns / 0.023 = 43478 turns on the secondary .
2. One has to know what Ampere is tolerated in the wire in a coiled fashion, there is no formula and must be deduced by experience. Then calculate the Ampere in the coil from the voltage and desired Resistance. A thin wire diameter will not tolerate a high Ampere.
R = U (Volt source) / I (Ampere desired to crossection of wire)
Find a chart that lists all the AWG (American Wire Gauges), or SWG (Standard Wire gauges)
Ex1
A ) I have a 230V AC supply and want 1 Ampere in the coil
B) I have a 12V DC supply and I want 0.5 Ampere in the coil
A) R = U / I = 230V / 1 A = 230 R ohm over the coil
be aware that the coiling geometry has a great play with the reduction factor ( powerfactor) cosinus phi. The more turns, the less is the cosinus phi value ( a High phi close to 1 is no reactive loss) . I estimate it to be cos phi = 0.5 . In an AC circuit the "actual" resistance is the Impedance. and when I desire 1 Ampere in the AC coil then I copy 230 R ohm to Z ohm . so R = Z. then calculate a new Resistance.
R ( recalculated) = Z * cos phi = 230 Z ohm * cos phi 0.5 = 115 R ohm
The resistance is half ! Meaning. I can have less turns and spend less wire on an AC coil, to obtain 1 Ampere in the coil !
B) For the DC coil it is more conventional.
R = U / I = 12V / 0.5A = 24 R ohm over the DC coil
3. Ohm per Meter : How many meters of wire will be consumed to obtain 115 R ohm ?
Then look at the chart for the different AWG or SWG wires and see the "Ohm per meter". Then calculate.
Meter of wire = Coil R ohm / AWG ohm per meter .
Lets say I want to use AWG#24 wire at 0.511 mm diameter. It is listed as 0.841 ohm per meter
Meter of wire = 115 R ohm / 0.841 ohm/m = 136 meter of wire total.
I usually then translate the meter into centimeter for handy measures.
There are 100 cm in 1 meter.
cm of wire = meter * E2 = 136 meter * 100 = 13600 cm of wire
4. Turns : Then I start to figure out the geometry of the coil. shall it be wide and short, or tall and narrow ? shall it be a solenoid, or a spiral coil or multilayered ?
First I must choose a diameter to work with. Maybe 5 cm diameter of the coil core. this depends on the size of the machine. Then I must find the circumference of the core, and calculate how long 1 turn will be.
O Circumference = Pi * 2Radius = Pi * Diameter = 5 cm * 3.14 = 15.7 cm
Finding the total number of turns will be as follows
Turns = Wire lenght in cm / O circumference = 13600 cm of wire / 15.7 cm = 866 turns on this paricular coil.
what I usually do is to perform a " blocking" of the coil I square the number and have equal number of turns tall and number of layers.
Coil block = SQRT 866 = 29
I then have 29 turns of wire for each layer, and 29 layers. making it a "block". I then sometimes multiply that number with a factor to make the coil slighly taller and thinner or slightly thicker. lets say I want it alittle thinner or fewer layers and more turns per layer. by a factor of 0.8.
Turns = 29 / 0.8 = 36 turns tall
Layers = 29 * 0.8 = 23 layers thick
the same number applies in total when multiplied 36 turns * 23 layers = 828 turns total , with some comma reductions. and I can add a layer perhaps to get it closer to 866 turns and then the Resistance will make a better match . Turns = 36 * 24 layers = 864 turns total
5. By knowing the diameter of the wire , for instance AWG#24 =0.511 mm . One can calculate the material dimensions of the coil. There are 10 mm in 1 cm.
Coil core height = 36 turns tall * 0.511 mm = 18.3 mm
Translate to cm = 18.3 * E-1= 18.3 * 0.1 = 1.8 cm tall .
The layers is done the same way.
However consider that the more layers are added the larger the circumference becomes. there fore I usually calculate the inner and outer layer and then find the average circumference. to be picky one can add that the circumference of the wire is 1 wire radius larger than the core radius. If your even more picky you can calculate the spiral displacement, that is 1 wire diameter for each spiral turn. And even more picky you can try to calculate the coil with the wires into the grooves of the former layer ! ( but that I found out is not really neccesarry) .
Turn Inner Diameter = core diameter + 1 wire diameter = 5cm + 0.511mm * E-1 = 5.0511 cm
Layer Circumference Inner = Pi * Diameter core + Diameter wire = 3.14 * (5cm + 0.511mmE-1) = 15.86 cm
Turn Outer Radius = n layers * Wire diameter = 24 * 0.511mm E-1) = 1.22 cm Radius
Turn Outer Diameter = 1.22 * 2 = 2.45 cm
Layer Circumference Outer = Pi * (D core + Turns outer Diameter) = 3.14 * (5cm + 2.45) = 23.4 cm
The average Circumference will be
O average = Turns Inner Diameter + Turns Outer diameter / 2 = 15.86 + 23.4 / 2 = 19.63 cm long.
To obtain the proper coil one needs to calculate back and forth , and make some coils and test them in a reality check. The first sort of rule of thumb is that the limitations of a coil is the Temprature. The temprature is given by the Ampere in the wire and the coils ability to cool off. A large surface on the coil will cool it off better, like a solenoid. Oils will also cool the coil. If the coil is too hot and the insulation melts, one needs to do either, increase the crossection of the wire, in so doing reducing the resistance, and one needs more turns to obtain the same resistance. Or Increase the resistance with the wire crossection already in use. Iron outside the coil circumference also reduces the Amperes and indirectly cools off the coil. If the coil is cold during operation, you can use a thinner wire or reduce the Resitance. I have a digital temprature or IR meter that gives an indication of the temprature. The other limitation of a coil is in the E-field or static field, Once high voltage is obtained the static will want to arc over the coil turns, particularely where the wires are crossing. and very voulnerable at the IN and OUT wires. that can cross over wires of the coil or parts of ground, inducing an arcing between the turns. Its therefore important to insulate the turns that is crossing the other wires perpendicular, an any axis. The coil and capacitor is therefore a path to master the polar fields of the B-field and E-field. These two fields separate themselvs from the other fields in physics, gravity for instance that may be a monopolar field, Gravity rejects no matter, and has no opposite pole. the electrons alone in a cathode ray also seems like a Monopole field, that attracts and recject the magnetic projection in respective terms. the electron is known for being a "monopole" of a negative charge. the Atom stripped of electrons is said to be of positive charge. together the Atom makes a dipole. If you ever philosopied on "Parallell dimensions" the static and magnetic and gravitational and Temprature are all different fields working at the same time. You dont have to go to outer space to experience a parallell dimension !
A mathematical digression.
When the formulas have certain symbols, they are expressing a specific object. to me it seems all math is based on the 3 basic ground shapes, and a combination of the following. The Square. The Triangle, and the Circle. the symbols applying to them is distinct. when these symbols are used. one can be shure these are the shapes that apples to describe the phenomena.
the Square : Lenghts. Addition, Subtraction, Multiplication and Division. Square root. Area, Cubes and Time.
the Triangle : Cosinus phi, sinius phi for right angled triangles, along with degrees of 180 ( half the degrees of a Square). Kathets and Hypothenus.
the Circle = Pi, radius, diameter. Spheres, Orbits and Fields. When a wheel of 1 lenght diameter rolls one rotation over the ground. The track measures 3.14 in lenght. Magnetic, Static, Tempraure, Light and Gravity fields all tend to be circular from the source, along with waves in water. No matter the shape of the radio antenna, light bulb ( unless it is directional, that limits its broadcast by reflectors or "parasitic elements" like in the Yagi antenna to enhance a desired direction). any wire or coil or even object dropped into water, the waves spread in circles. so they should have the circle symbols in them. I dont know if this is an important question or not but, when is the field so strong that it forms a spherical body around its source . that is how strong must a magnetic field be to form a spheric magnetic field when the source is a cylindrical coil ? how large must the Static field to form a sphere when the plates are an area plate of a certain measure ?
Now that is what I want to say for now.
Hope you enjoy coiling. this is to inspire and share methods of a very interesting topic !
The Coil and Capacitor is practically what runs the "modern society".
AC is frequenctial current. and can be ordered into 4 different triangles.
Each triangle respond to the Pythagoras formulas, with one hypothenus, and two kathets. The kathets form a 90 degree angle.
The Horiosontal kathet represent the Resistive or DC domain of the circuit (real).
The Vertical kathet represent the AC loss or reactive values (imaginary) .
The Hypothenus is however the "actual" value during AC operation.
In my own terminlolgy.
Triangle 1 : Hypothnus = U = Volts, Horizontal kathet = U_R Volt Resistive. Vertical kathet = U_X Volt Reactive
Triangle 2 : Hypothnus = I = ampere. Horizontal kathet = I_R Ampere Resistive. Vertical Kathet = I_X = Ampere Reactive
Traingle 3: Hypothenus = S = VA. Horizontal kathet = P = Watt "P for Power". Vertical kathet = Q = var Volt ampere reactive or "Q for Quality" in radioscience this is "damping" in the antenna or coax. In audio filtering it is the wide or narrow band of the frequency specter through the speaker, on the electric guitar this has a knob named "Tone", see Humbucker coils. On Digital Sequencers and EQ`s there is a button called Q, and this shapes the curve wide or narrow, allowing just a selected frequenctial band pass through the speakers. This is also the factor that can be tuning the coil into electrical resonance or an "electrical echo" between the terminal ends, by adjusting the capacitor. I would interpret a large value of Q= var as a Low damping, allowing most of the various frequencies from the generator or musical instrument pass. whereas a coil with Low Q= var has a high damping, meaning the coil allows passage for just a narrow band of frequencies ( it might be the other way around ). The Q = var in the AC formula is not the same as Q= coloumbs in the capacitor. Q (coloumbs ampere second) = C (farads) * U (volt) . it seems, but they also seem related, needs more investigation.
Triangle 4 : Hypothenus = Z Impedance, resistance with frequency. Horizontal kathet = R Ohm Resistive. Temprature losses are in the Resistive domain. Vertical Kathet = X Reactance, A collecion of losses in self induction and core hysteresis (remagnetisation of the Iron, due to magnetic saturation . The electrons cant keep up the frequenctial shifts from North to South, and lag in the middle of the Iron material, and cancels eachothers polarisations out). In other words, the Facoult (Eddy) currents are counter acting the magnetic polarisation in the Iron. Like a paddle in the water, can set up a small tornado or whirl in the water , resisting the paddle to move backwards agains the rotation of the swirl.
When a certain coil is constructed and tested. One can calulate the cosinus phi, and when drawing the 4 triangles, all the triangles shall share the same cosinus phi value and angles. It is for a reason that Pythagoras formulas may be the most useful formulas known to humanity, For it can be used in music and electrical inducstry as to coils and electric motors. See for instance the note A 440 Hz * SQRT2 = 440 * 1.41 = 622.2 Hertz. That is a D# in the 12 tet temprament system or 6 semitones up from note A. Playing the A and D# on the guitar or a keyboard practically plays a Likesided triangle, that is bothe the Kathet "string A" and Hypothenus "string D#". It doesnt produce a beautiful harmony and was back in the days bamnned by the Christians this particular chord, for mystical reasons !Pythagoras is also credited with the phrase " Numbers is the origin of Gods and Demons". In my philosophy a God is a harmonic realtionship, and a demon is a disharmonic relationship. The word "Arch" would be handed over to the readers imagination to conceptualize. Whether Pytagoras was a person from Hellas or a group of people, belonging to a school of mathematics, most certainly inherited much of their teachings from Farao in Egypt, it may be the concepts of PTH tha Egyptian God of engeneering, however it remains uncertain. The spelling of their names is very similar Ptha and Pythagoras.The AC generator is practically a musical instrument, and often called a "Tone Generator" or "Harmonic Generator".
These are the formulas I have obtained.
From cross calculating the values from the schoolbook or ground book of basic electricity and my own measures. In the chapter of "the electric grid", or maybe "installations for light control"." effect vector diagrams", phase compensation.
Keep in mind that most of these values are obtained only after the model is built. the Volts and Resistance may be the only "safe" values from a desktop perspective, that is the socket or supply voltage, and the ohm per meter on the wire crossection. Keep in mind that as the temprature increase of the wire the resistance also increase, so Resistance is only a constant as long as the temprature is constant. The temprature loss that is understood as a Blackbody radiation, the heat loss can actually be translated into IR or infra red loss ! Infra red is a "electromagnetic" ( or radiant ) waveform that transmits heat with the speed of light, but the wavecompression over a distance of vacuum isnt in itself hot. its heating action only applies when a molecule or atom is being struck. I think the IR adds vibration to the atoms or molecules, and the friction between them transmit a heat wave that is again sensed by the nerves in the fingers or the environment. I think that the IR wave is generated by the nucleus, and not the electrons, for It would not be impossible that a static object, or an object stripped of electrons become hot. It can be argued that the Amperes that are electrons that travel over a wire creates heat, and that is true in my opinion. But I counter that argument by claiming that its the atoms that are being stirred by the electric motion and this way the atoms in the copper wire vibrate until their solid bonding turn fluid. Aother argumetn is how can a DC current generate a Infra red alternating waveform in the gigahertz range, that is low frequency light waves or heat ? Yet another interesting thing with heat is that almost all materials generate the same waveform in the heat spectrum. Temprature is also very unlike a magnetic field, for a cup of hot water can be turned upside down to become cold ! like a opposite polarity of a magnet. sharing some characteristics with the uncoprehensible complexity of gravity. Gravity atracts everything, and doesnt repell any material, One can turn an object sideways or upside down, there is no change in the gravity field, only the number of particles determine the gravity, in my understanding . a statemmetn may be that soem fields have polarity and others have not. the static and magnetic fields have polarities, Temprature and Gravity does not have polarities.
Its still quite a challenge ( If possible at all) to calculate the cosinus phi or the Reactive values of a Secondary coil with just knowing the Ampere and Resistance, without knowing the Volts of the secondary. For that I need a Voltage Divider, to reduce the voltage so the digital Volt meter wont be destroyed . The cosinus phi depend on the coiling geometry, frequency, self induction and the capacitance. A certain man named Nikola Tesla whose excellence remain hidden deep in the future, managed to make his coils with the proper capacitance in the coil itself, not needing an external capacitor ! Different coiling geometries might be a long and narrow coil (solenoid) or short and wide (spiral coil), Or more usual a coil with several layers of wire.
Ampere
I = U / Z = S / U = Q / U_X = P / U_R = I_R / cos phi = I_X / sin phi = SQRT Q/X = SQRT S/Z = SQRT P / R = P / (U * cos phi) = Ampere
I_X = U_X / Z = Q / U = sin phi * I = SQRT I^2- I_R^2 = Ampere Reactive
I_R = U_R / Z = P / U = cos phi * I = SQRT I^2 - I_X^2 = ampere Resistive
Volt
U = P / I_R = Q/ I_X = S / I = U_R / cos phi = U_X / sin phi = U_R^2+U_X^2 = I * Z = I *R / cos phi= Volt
U_X = Q / I = Z * I_X = X * I = U * sin phi = SQRT U^2 -U_R^2 = Volt Reactive
U_R = P / I = Z * I_R = R * I = U * cos phi = SQRt U^2 - U_X^2 = Volt Resistive
Watt (Effect)
S = P / cos phi = U * I = Z * I^2 = SQRT P^2+Q^2 = U^2 / Z = VA (Volt Ampere)
Q = U * I * sin phi = U * I_X = X * I^2 = U_X * I = sin phi * S = SQRT S^2 -P^2 = var
P = U * I * cos phi = U * I_R = R * I^2 = U_R * I = cos phi * S = SQRT S^2 - Q^2 = U_R^2 / R = Watt
Resistance
Z = U_R / I_R = U / I = R / cos phi = X / sin phi = SQRT X^2 + R^2 = S/I^2 = U^2 / S = Z ohm, impedance, (Resistance with frequency)
X = U_X / I = sin phi * Z = SQRT Z^2 -R^2= Q / I^2 = (U_X^2 / Q...?) = X Ohm Reactance
R = U_R / I = cos phi * Z = SQRT Z^2-X^2 = U_R^2 / P = P / I^2 = R Ohm Resistance
Power Factor
cos phi = P / S = R / Z = I_R / I = U_R / U = tan^-1 (I_X / I_R)
sin phi = Q / S = X / Z = I_X / I = U_X/ U
Angle Degrees
Cos phi = cos^-1 (P/S) = sin^-1 (Q/S)
sin phi = cos-^1 ( Q/S) = cos ^-1 (P/S)
Approximations of Z impedance
Z = (U/I from DC) / cos phi estimate = R / cos phi estimate
Approximation of I ampere
I = (P/U from DC) / cos phi estimate
The following formula for henry is rearranged from a capacitor / coil phase compensation formula in the common science (my electrical groundbook) , known as
X ohm = 2 * pi * hz
by dividing both sides of the = sign with 2 * Pi * hertz one results in this :
X ohm / ( 2 * pi * hz) = 2 * pi * hz * L / (2 * pi * hertz)
the similar values are stroked out from the equation and the result will be as follows.
X ohm / 2 * pi * hz = L / 1
L = X ohm / 2 * pi * hz = henry
Id be happy to get a comment on that, for I do not know exacly what that number or value means ...
Likewise the Cap can be calculated like this
X ohm = 1 / 2 * pi * hz * C ( farads)
multiply both sides of the = sign with 2* pi * hz and get
X ohm * ( 2 pi * hz ) / 1 = 1 * ( 2 * pi * hz ) / 2 * pi * hz * C
1 / C = 2 * pi * hz * X ohm
One can flip it around once more and get
C farad = 1 / 2 * pi * hz * X ohm
Phase Compensation :
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14.08.2016
Magnetic Field Strenght
Interpreting the formulas is a study in itself. and concerning the H = A/m. Noted as Magnetic field strenght.
H = magnetic field strenght measured in Ampere per meter. ( seemingly not H = henry... !)
A/m = Depending on the formula. The value is a 1 dimensional line either in the center of the core, measured in meter between the first and the last turn. Or the Ampere per diameter of the wire, or the Ampere per Circumference of the wire.
This formula express the Ampere Turns per Meter as one value for "magnetic field strenght".
H (coil center axis) = I ( Ampere ) * n turns / l lenght in meter = A/m ( a central line in the coil core )
This formula does not concerne the diameter of the coil, and has no value for width; that must be calculated using another formula. In my interpretation of this formula, since there is no diameter, The coil is wound on a hair thin core, And after some thought the radius or diameter of the cylinder may not play any difference in this formula. the radius determines the circumference of the coil and thus relates to the resistance of the wire on the coil. Even tho the drawings accompanying the formula usually render a nice and large coil, the formula is rather illusive, if not unusable ! neither does it concerne the crossection and the temprature of the coil.
1st attempt (abandoned go to 3rd attempt )
I just discovered a method to transform a multi layered coil into a Solenoid. Lets say I have a coil that is 10 turns tall * 10 layers thick, conveying 2 Amperes in the wire. the Ampere Turns will be :
Coil Ampere Turns = 10 turns * 10 layers * 2 A = 200AT
Now I divide away the layers, making it a 1 layer coil, then multiply the ampere by the division factor. the factor is the number of layers
10 layers / 10 factor = 1 layer
2 ampere * 10 factor = 20 Ampere
Solenoid Ampere Turns = 10 turns tall 1 layer thick * 20 Ampere = 200AT
Lets say the coil is 5 cm tall
l ( lenght in meter) = 5 cm = 5 * 10^- 2 = 5E-2 = 0.05 meter
H (coil center axis) = I * n ( turns) / l (lenght meter) = 20A * 10 turns tall / 5cm E-2 = 200 / 0.05meter = 4000 A/m
This is the same as
H (coil center axis) = I * total turns / l = 2A * 10 turns * 10 layers / 5 cm E-2 = 200 / 0.05meter = 4000 A/m
so the conversion from a multi layered coil to a solenoid is actually not neccesarry.
2nd attempt ( abandoned . go to 3rd attempt)
In my quest for understanding the formulas another interpretation has presented itself. It deviates slightly from the conventional formula but use them as construction basis. And I have come to form 3 formulas, one for the solenoid, and multilayered coil that is longer than it is wide : N Turns > N Layers. One formula for when the coil is squared or block coil : N Turns = N Layers , and another when the coil closes into a spiral coil : N Turns < N Layers. In my mind the coils magnetic field must be weaker the longer it is, but equally weaker the wider it is if its a spiral.
Lets say I have a coil of 900 turns, carrying 2 amperes. the wire diameter is 1mm
I = 2A
Wire Ø diameter = 1 /1000 = 0.001 meter
900 turns in meter = 900 turns * 0.001 meter = 0.9 meter long coil
30 turns in meter = 30 turns * 0.001 meter = 0.03 meter long (or tall)
1 turn = 1 turn * 0.001meter = 0.001 meter long
conventional formula
H = I * N turns / lenght meter
H = 2A * 900 turns / 0.9 meter = 2000A/m
What if I want to have 2 layers and half the lenght ?
I came up with this formula
Solenoid single layer
H (turns > layers) = (I * N turns * N Layers) / (coil lenght meter / coil width meter)
H = 2A * 900 turns * 1 layer / (0.9m long / 0.001m wide) = 1800AT (ampereturns) / 900=
H = 1800 AT / 900 = 2 A/m
This value is significantly lower than the conventional number ! but then again consider this coil is 90 cm long ! ( (90 cm /30.48 = 2.9 imperial feet) . and 1 layer thick. Or expressed more figuratively, the diameter of the wire is the radius of the coil, making the coil 2 mm in diameter. There is NO chance the turn on the far end can have any magnetising effect near the projection pole on the other side. thee donut hole or cylinder core or pole projection is a name I am now calling "Projection face". It also seems to me that the donut hole of the coil has the strongest magnetic field concentration. and the magnetising target, usually Iron, should match the diameter of the coil core, or projection face, not the entire coil with the windings, just the hole in the middle. that statement is based on when I have a coil with amperes in it. The iron filings are mostly attracted to the inside of the coil, It may be the circumference of the outer turns are greater, making the filed lines tight at the inner turns. I want to add that I measured about 320Ampere Turns to lift 1 gram of sheet iron ! and it seemed the more close the iron was shaped the inner hole diameter the better the attraction became. And I need about 30Ampere turns to get a feeble response in iron filings at the center of a 1 cm diameter coil, the 30AT thus creates a magnetnic response to iron filings at about 5 mm or so. Leading to a formulation that if I have another coil of the same measure, more than 0.5 cm away , the magnetic field wont add to the former, so distance of the turns makes a big differance. The coil above calculated has neither has a radius or a diameter. so its basically a wire coiled on a core less than a hair thick.
Solenoid ( 2 layers ) multilayered
Turns = 900 / 2 = 450 turns
layers = 1 * 2 = 2 layers
Lets say I want to half the lenght and instead have 2 layers.
H (turns > layers) = (I * N turns * N Layers) / (coil lenght meter / coil width meter)
H = (2A * 450 turns * 2 layers ) / (450 turns * 0.001meter / 2layers * 0.001meter ) =
H = 1800 AT / (0.45 / 0.002) = 1800 AT / 225 = 8 A/m
By making the coil shorter and increasing the layers the A/m increases too, while the number of turns are kept the same. As expected.
Now the block coil or Squared coil where the Turns long is equal to the number of layers
Block (squared) coil ( N turns = N Layers)
turns = SQRT 900 = 30 turns long
Layers = SQRT 900 = 30 layers wide
H (turns = layers) = (I * N turns * N Layers) / (coil lenght meter / coil width meter)
H = (2A * 30turns * 30 layers) / (30turns * 0.001 / 30layers * 0.001 )
H = 1800 AT / 1 = 1800 A/m
Here one can see that the number under the fraction line becomes 1. and that is the largest number that can appear in the formula. so the block or squared coil has the maximal A/m for a given coil geometry.
then lets increase the layers even more and approach a spiral coil. In my understanding the A/m cant become more than the solenoid or the block coil, for all coils have an Ampere Turn of 1800 AT in this examples. the way I worked around it is to reverse the number beneath the fraction line once the turns are less than < the Layers.
spiral coil multilayered
Turns = SQRT 900 = 30
Layers = SQRT 900 = 30
And I want it to be double as thick as it is long, using a factor of 0.5
Turns = SQRT 900 * 0.5 = 15 turns long
Layers SQRT 900 / 0.5 = 60 layers wide
double check = 15 turns * 60 layers = 900 turns total
H (turns < layers) = (I * N turns * N Layers) / ( coil width meter / coil lenght meter /)
PS. Notice here that the width and lenghts are switched under the fraction line !
H = (2A * 15 turns * 60 layers) / (60 layers wide * 0.001m / 15turns long * 0.001m)
H = 1800AT / 0.06 / 0.015) = 1800AT / 4 = 450A/m
spiral coil
turns = 1
layers = 900
H (turns < layers) = (I * N turns * N Layers) / ( coil width meter / coil lenght meter /)
H = 2A * 1 turn * 900 layers ) / ( 900 layers wide * 0.001 / 1 turn long*0.001) =
H = 1800AT / (0.9m / 0.001m ) = 1800 AT / 900 = 2A/m
From this formulas a spiral coil of 900 turns wide, is equally poor in its Ampere per meter than a long solneoid of 1 layer and 900 turns ! To me it makes sense. Consider the actual size of the spiral coil above mentioned. its radius is 900 turns each turn is 1 mm making it a disk about 1.8 meters in diameter ( just under 6 feet in diameter) ! There is no chance the outer turn can magnetise all the way into the center turn with 2 amperes in the wire ! But it might be wrong. And I presume much better formulas can be devised. the problem is that it cant be used with conventional A/m values. but then again I have not seen any general formula concerning the multilayered coil ! the benefit of this approach is that it can be applied to both B = tesla, and L = henrys in the same way. When the A/m is determined, then one can move on to find the desired Projection face (projection pole), or opening of the donut hole, or diameter of the coil. to fit the generator pole or the target it is to magnetise. In so doing also determining the Resistance of the coil, and lenght of wire to spend.
Summary
Solenoid (coil is longer than its
thickness) = turns > layers
H = (I * N turns * N layers) / ( coil
lenght meter / coil width meter )
Squared or Block coil : turns = layers
H = (I * N turns * N layers) / 1
Spiral coil ( coil is thicker than its
long) : turns < layers
H = (I * N turns * N layers) / ( coil
width meter / coil lenght meter )
PS. The formulas will give the same A/m no matter what wire crossection one uses. The value for A/m will be the same number for a 1 mm wire , a 16 mm^2 wire or a 240cm^2. I dont know if that is true in reality. However increasing the crossecion reduses the temprature and resistance.
Radius from wire Crossection 16 mm^2 wire = SQRT 16 / pi = 2.25 mm radius
PS. The formulas will give the same A/m no matter what wire crossection one uses. The value for A/m will be the same number for a 1 mm wire , a 16 mm^2 wire or a 240cm^2. I dont know if that is true in reality. However increasing the crossecion reduses the temprature and resistance.
Radius from wire Crossection 16 mm^2 wire = SQRT 16 / pi = 2.25 mm radius
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3rd attempt.
25.09.2016
I have chose to abandone the above formulas, named attempt 1 and attempt 2 . And replace them with the following below. In this 3rd attempt to understand the H = A/m, B = u0 * H= tesla and the L = henry. I have also chosen to rename the suffix in the H = A/m into H = Ampere Turns / per coil lenght in meter. I had a hard time understanding what actually is "Ampere per meter" . then suddenly I realised it had to be Ampere Turns per meter. but not per meter. but per coil lenght, measured in metric units. The formula of the "attempt 2" where I divided the Ampere * Turns / lenght * width gave a rediculus large value and cant be true. I then figured that a Solenoid of 1 layer had to be half the value of a 2 layered coil. I write it down here so I know where they are .
Unfortunately no reduction factor for
the coil width, only a reduction factor for the lenght.
Turns = turns per each layer
I = Ampere
I = Ampere
l = lenght of coil in meter. Lenght is
measured between the north and south projection poles.
A = area of the projection pole, in meter.
A = area of the projection pole, in meter.
AT/m =A/m Ampere Turns per coil lenght in
meter ( replacing A/m, when the formula multiplies Amperes and turns
).
B = magnetic field strenght over the
total region, or total magnetic field radiating from a coil.
Flux = certain area of the magnetic region.
Flux = certain area of the magnetic region.
L = coils ability to «store» a
magnetic field. Notice there are no Amperes in the L formula. And since there is no Amperes in the L = henry formula I suspect this formula is not actually the coils ability to "Store" a magnetic field, but rather to "recieve" a megnetic field. thus implying the use of this formula is onto antennas and secondary coils . The B = tesla would be for the primarys or electromagnetic coils and permanenet magnets, that have Amperes that creates a magnetic field.
u0 = 4 * pi * E-7 ( dont ask, it has
something to do with coloumbs torsion experiment)
Cloumbs Torsion Balance : Coloumbs Torsion Balance . I also suspect that the word "torsion" is related to the word "Tork" or rotational force. And so it is. Torsion is to twist a material around its own lenght axis, a rope, rubber or metals. Tork is to motivate a rotation of a rotor or cogs, on an axel with jewel (in clocks, rubys and diamonds) or rollerbearings in motors. And example of both tork and torsion would be a nut on a bolt. by thightning the nut so hard that the bolt that its head break off. too much tork ( in newtonmeter) is applied and the torsion toleranceof the bolt material is exeeded, and the bolt is destroyed.
Back to the u0 = 4pi, I question what is the geometry of 4pi ? and it occurs to me that Coloumb worked with spheres, and if there is a Pi there is a circle involved, so the geometry is definitly circular. and it shows that Pi * 4 = Pi * 2^2, that is the Area of a Sphere. The radius is 2 units of 1. and if that is the case that 4Pi is the same geometry as Pi * 2^2, the suffix of units should be if meter m^2. the value of 4Pi may also be a circumference where the diameter is 4 units of 1, making it a linear or 1 dimensional value, in meter Circumference = Pi * 4 meter diameter = 12.56 m . It is then appearing another question, magnetism or the B = tesla is not an Area, In my opinion a Volume. the magnetic value should penetrate the iron core or coil uniformly, and once the magnetism is outside the volume the value fades out. How come a surface or area is confused into the permeability (the materials ability to magnetise), when it should be a volumetric value? and what geoemtry isdielectric constant e0 = 8.85 * 10-12 ? That is concerned with the Charge on surfaces or areals ? Checking the Wiki on 4Pi I read of Solid angles and a thing called Steredians, and the Surface of a Sphere is 4 * Pi * r^2 = units^2, true to 12.56 when the radius is 1. I interpret this as the u0 = permeability is the area of a sphere, and the Radial values is the H= A/m ( or ampere turns per meter). but that doent either make sense for the formula for B = tesla = u0 * H, And not u0 * H^2. well .
e0 = vacuums ability to permit a static field. See that its the u0 magnetic permeability ( vacuums ability to magnetise or allow magnetic lines) multiplied with the speed of light, divided by 1.
e0 = 1 / u0 *c^2 = 1 / (4*pi*E-7) * 299 792 454^2 = 1 / 1.129*E11 = 8.85*E-12 F/m
Cloumbs Torsion Balance : Coloumbs Torsion Balance . I also suspect that the word "torsion" is related to the word "Tork" or rotational force. And so it is. Torsion is to twist a material around its own lenght axis, a rope, rubber or metals. Tork is to motivate a rotation of a rotor or cogs, on an axel with jewel (in clocks, rubys and diamonds) or rollerbearings in motors. And example of both tork and torsion would be a nut on a bolt. by thightning the nut so hard that the bolt that its head break off. too much tork ( in newtonmeter) is applied and the torsion toleranceof the bolt material is exeeded, and the bolt is destroyed.
Back to the u0 = 4pi, I question what is the geometry of 4pi ? and it occurs to me that Coloumb worked with spheres, and if there is a Pi there is a circle involved, so the geometry is definitly circular. and it shows that Pi * 4 = Pi * 2^2, that is the Area of a Sphere. The radius is 2 units of 1. and if that is the case that 4Pi is the same geometry as Pi * 2^2, the suffix of units should be if meter m^2. the value of 4Pi may also be a circumference where the diameter is 4 units of 1, making it a linear or 1 dimensional value, in meter Circumference = Pi * 4 meter diameter = 12.56 m . It is then appearing another question, magnetism or the B = tesla is not an Area, In my opinion a Volume. the magnetic value should penetrate the iron core or coil uniformly, and once the magnetism is outside the volume the value fades out. How come a surface or area is confused into the permeability (the materials ability to magnetise), when it should be a volumetric value? and what geoemtry isdielectric constant e0 = 8.85 * 10-12 ? That is concerned with the Charge on surfaces or areals ? Checking the Wiki on 4Pi I read of Solid angles and a thing called Steredians, and the Surface of a Sphere is 4 * Pi * r^2 = units^2, true to 12.56 when the radius is 1. I interpret this as the u0 = permeability is the area of a sphere, and the Radial values is the H= A/m ( or ampere turns per meter). but that doent either make sense for the formula for B = tesla = u0 * H, And not u0 * H^2. well .
e0 = vacuums ability to permit a static field. See that its the u0 magnetic permeability ( vacuums ability to magnetise or allow magnetic lines) multiplied with the speed of light, divided by 1.
e0 = 1 / u0 *c^2 = 1 / (4*pi*E-7) * 299 792 454^2 = 1 / 1.129*E11 = 8.85*E-12 F/m
H = ( I * N turns / l ) * N layers =
AT/m
B = u0 * ( I * N turns / l ) * N layers
= tesla
L = (u0 * N turns^2 * N layers * A) /
l = henry
Find the N turns from an existing coil.
1. Measure up the lenght of the coil in
millimeter.
fx. 57 mm long
2. find what wire diameter it is in mm.
fx. 0.511 mm Ø diameter
3. Divide coil Lenght on wire diameter
fx. 57 / 0.511 = 111 turns long
4a. Measure up the width of the coil and start on step1.
4b. If you have the total number of
turns and want to know the N layers
Divide the total turns on the number of
turns per layer
fx. 1000 turns total / 111 turns per
layer = 9 layers
N turns total = 111 * 9 = 999 turns.
Spiral Displacement of Wire
If your really picky, and have a very long wire. As the wire is coiled around the core. Each turn as it is put beside the other, the lenght of each turn increases by 1 wire diameter, The turn lenght is equal to the circumference of the core pluss half the diameter of the wire pluss another diameter of the wire as the turns are put beside one another. When many wires are coiled this tiny amount of wire may accumulate some additional Ohms or resistance. I have developed a formula for N number of turns . A description to the formula. One loop turn of wire around a core in 3 dimensions, can be broken down or illustrated or rather modelled by having a piece of paper that is square, then draw a diagonal line with a pencil on that paper. Rolling a piece of paper into cylinder and a perfect Sinius is formed over the paper cylinder. If you havent done it before, its an act of magic ! The 2 dimensional Diagonal, is a 3 dimensional Sinius curve. Therefore a diagonal and the square format, can be used to determine the wavelenght ( or rather the lenght of the sinius shape...!), as well as turns of wires around a cylinder, And logically related to Square root of 2. Thus Pythagoras formula can be used. ( I have yet to figure out a proper formula for a spiral . That is very difficult to determine the lenght of a spiral wire .) this formula only applies for the first layer. I have managed to obtain a set of 5 formulas that needs to be used in succession as the layers progress. but its totally uneccesary.
X = lenght of 1 turn, or circumference of the core, pluss half a diameter if the first layer.
Y = total lenght of the core, lenght measured between the pole projection faces.
Z = total lenght of spiral wire
For 1 turn.
Z = SQRT X^2 + Y ^2
for 2 turns
Z = (SQRT X^2 + (Y/2)^2) * 2
for 8 turns
Z = (SQRT X^2 + (Y/8)^2) * 8
For any turns N turns
Z = (SQRT X^2 + (Y / N turns))^2 * N turns
Example
Core diameter = 3 cm
Core circumference = pi * 3 = 9.42 cm = X
Coil height = 10 cm = Y
N = 1000 turns
Z = SQRT X^2 + (Y/1000)^2 * 1000
Z = SQRT 9.42^2 + (10/1000)^2 * 1000
Z = (SQRT 88.82 + 0.0001) * 1000
Z = 9.42444 * 1000 = 9424 cm long wire ( then obtain the Ohm per meter.)
This version is abit shabby, for the wire diameter is not included. Needs an update that inkludes the wire gauge . You gonna calculate . or coil ?
end update 25.09.2016
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Magnetic field strenght in the center of one winding.
In this formula one can "focus" the magnetic field from weak to strong by narrowing down the diameter of the coil. Making the poles more intense.
r (radius in meter) = 2.5cm = 2.5E-2
What this formual express is the Ampere / Diameter . for 2 * Radius = 1 Diameter
H (turn) = I / 2 pi * radius in meter
H (turn) = 2A / 2 * pi *2.5E-2 = 12.73 A/m ( Magnetic stenght over the diameter of the wire )
Version with the multilayered coil "transformed" into a solenoid.
H (layer ) = 20A / 2 * pi * 2.5E-2 = 127.3 A/m
Magnetic Field Strenght in a point outside a straight conductor
This formula Express Ampere per Circumference.
r = radial distance outside the conductor in meter, lets say 0.5 cm
H = I / 2 pi * r
H = I / pi * radius * 2
O circumference = Pi * Radius * 2
H (turn) = 2A / 2 * pi * 0.5cm E-2 = 0.0063A/m ( Magnetic strenght over a circumference around the conductor)
Add 10 turns from the multilayered coil
H (layer) = 20A / 2 pi * 0.5cm E-2 = 0.063 A/m
This is the same as multiplying in 10 more turns
H (layer ) = (2A / 2 * pi * 0.5cm E-2) * 10 turns = 0.0063 * 10 turns (spiral) = 0.063 A/m
Now presume that the multilayered coil is only having 1 turn and 1 layer, but the same volume of copper mass ! Just a block of copper coiled 1 turn around a core. that is a coil with no turn subdivisions. A bus bar in a loop.
The coil origionally has 10 turns * 10 layers = 100 turns * 2 Ampere = 200 AmpereTurns
Now divide away all the turns and layers and use the division number to multiply into the ampere.
100 turns / 100 = 1 turn coil
2A * 100 = 200A
H ( coil ) = 200A / 2 * pi * 0.5 E-2 = 6366 A/m at 0.5 cm distance from the coil windings, supposedly. Then you can ask yourself. what do I do with that number ?
Kirchoffs Parallell coppling
R = 1 / (1 / R1 + 1 / R2 + 1 / R3) = 1 / ( 3 / R_tot ) = ohm
R1 = 10 ohm
R2 = 20 ohm
R3 = 30 ohm
By having a parallell coppling one practically increase the crossection and the Ohm is reduced, compared to a series coppling that adds the resistance and is a natural adding value. The parallell is therefore a natural division . I see it as 2 terminal lines that are bridged with "pipes" of unequal thickness conveying water (Ampere) between the potential (Volt) .
Parallell Circuit
Terminal 1 Terminal 2
| |
| |
|.......10 ohm.......|
| |
|.......20 ohm.......|
| |
|......30 ohm........|
Find the common multiplum of the Ohms
10 = 2 * 5 -> * 2 * 3
20 = 2 * 2 * 5 -> * 3
30 = 2 * 3 * 5 -> * 2
Multiplum = 2 *2 * 5 * 3 = 60
Kirchoff parallell = 1 / (1*2*3 / 10 ohm* 2 * 3 + 1*3/ 20 ohm* 3 + 1*2/ 30 ohm * 20 ) = 1 / (6 /60 + 3/60 + 2/60 ) = 1 / (6+3+2 / 60 ) = 1 / (11 / 60) = 5.45 ohm
As far as I know the schoolbook and conventional formulas does not have the "1 / " (1 / R1 + 1/ R2). ontop, therefore making a confusion in the end result. the conventional formula suggest one has to flip the Numerator and denumerator of the fraction like this
Conventional Parallell = 1 / 10 ohm + 1 / 20 ohm + 1/ 30 ohm = 6 / 60 + 3 / 60 + 2 / 60 = 6 + 3 + 2 / 60 = 11 / 60 => magic flipover => 60 / 11 = 5.45 ohm. I just could not understand how on earth 11/ 60 = 60 / 11 ! and even worse it gives the correct answer to the measure . This is however solved by putting it like this 1 / (11 / 60 ) = 5.45 ohm . In my opinion that should be considered in the electrical teachings.I wouldconsider the coil as the most useful tool for what modern life concernes. And after a while of making coils, youll be counting turns in your sleep !
Planning out a coil
This is the way I do it usually. I start with knowing the supply voltage. Lets say a 12V or 230V source. Then I plan it using DC current, then apply the cosinus phi later on if its a AC coil. I have a number of steps I do.
1. Start by knowing the formula of the ideal transformation if its a transformer. A motor coil is practically also a transformer. Unless permanent magnets are used. the usefulness of this formula is to approximate the number of turns on the secondary coil, when considering a transformer, the unusefulness is that its ideal and not considering the temprature losses. losses over distance between the coils or reactance in the coils
k ( coiling constant) = U1 / U2 = N1 / N2 = I2 / I1
Transformer
U1 = Volt primary
U2 = Volt secondary
N1 = Turns Primary
N2 = Turns secondary
I1 = Ampere primary
I2 = Ampere secondary
To know the number of turns on the secondary. Lets say I want 10000V or 10kV on the secondary and have a 230V AC supply. how many turns on the secondary. In this case I must presume that the ampere in the primary is low enough not to overheat the coil. and large enough to encapsulate the entire secondary with a magnetic field. Lets assume that I have 1000 turns on the primary, N1 = 1000 turns.
k = U1 / U2 = 230V / 10 000V = 0.023
N2 = N1 / k = 230V / 0.023 = 1000 turns / 0.023 = 43478 turns on the secondary .
2. One has to know what Ampere is tolerated in the wire in a coiled fashion, there is no formula and must be deduced by experience. Then calculate the Ampere in the coil from the voltage and desired Resistance. A thin wire diameter will not tolerate a high Ampere.
R = U (Volt source) / I (Ampere desired to crossection of wire)
Find a chart that lists all the AWG (American Wire Gauges), or SWG (Standard Wire gauges)
Ex1
A ) I have a 230V AC supply and want 1 Ampere in the coil
B) I have a 12V DC supply and I want 0.5 Ampere in the coil
A) R = U / I = 230V / 1 A = 230 R ohm over the coil
be aware that the coiling geometry has a great play with the reduction factor ( powerfactor) cosinus phi. The more turns, the less is the cosinus phi value ( a High phi close to 1 is no reactive loss) . I estimate it to be cos phi = 0.5 . In an AC circuit the "actual" resistance is the Impedance. and when I desire 1 Ampere in the AC coil then I copy 230 R ohm to Z ohm . so R = Z. then calculate a new Resistance.
R ( recalculated) = Z * cos phi = 230 Z ohm * cos phi 0.5 = 115 R ohm
The resistance is half ! Meaning. I can have less turns and spend less wire on an AC coil, to obtain 1 Ampere in the coil !
B) For the DC coil it is more conventional.
R = U / I = 12V / 0.5A = 24 R ohm over the DC coil
3. Ohm per Meter : How many meters of wire will be consumed to obtain 115 R ohm ?
Then look at the chart for the different AWG or SWG wires and see the "Ohm per meter". Then calculate.
Meter of wire = Coil R ohm / AWG ohm per meter .
Lets say I want to use AWG#24 wire at 0.511 mm diameter. It is listed as 0.841 ohm per meter
Meter of wire = 115 R ohm / 0.841 ohm/m = 136 meter of wire total.
I usually then translate the meter into centimeter for handy measures.
There are 100 cm in 1 meter.
cm of wire = meter * E2 = 136 meter * 100 = 13600 cm of wire
4. Turns : Then I start to figure out the geometry of the coil. shall it be wide and short, or tall and narrow ? shall it be a solenoid, or a spiral coil or multilayered ?
First I must choose a diameter to work with. Maybe 5 cm diameter of the coil core. this depends on the size of the machine. Then I must find the circumference of the core, and calculate how long 1 turn will be.
O Circumference = Pi * 2Radius = Pi * Diameter = 5 cm * 3.14 = 15.7 cm
Finding the total number of turns will be as follows
Turns = Wire lenght in cm / O circumference = 13600 cm of wire / 15.7 cm = 866 turns on this paricular coil.
what I usually do is to perform a " blocking" of the coil I square the number and have equal number of turns tall and number of layers.
Coil block = SQRT 866 = 29
I then have 29 turns of wire for each layer, and 29 layers. making it a "block". I then sometimes multiply that number with a factor to make the coil slighly taller and thinner or slightly thicker. lets say I want it alittle thinner or fewer layers and more turns per layer. by a factor of 0.8.
Turns = 29 / 0.8 = 36 turns tall
Layers = 29 * 0.8 = 23 layers thick
the same number applies in total when multiplied 36 turns * 23 layers = 828 turns total , with some comma reductions. and I can add a layer perhaps to get it closer to 866 turns and then the Resistance will make a better match . Turns = 36 * 24 layers = 864 turns total
5. By knowing the diameter of the wire , for instance AWG#24 =0.511 mm . One can calculate the material dimensions of the coil. There are 10 mm in 1 cm.
Coil core height = 36 turns tall * 0.511 mm = 18.3 mm
Translate to cm = 18.3 * E-1= 18.3 * 0.1 = 1.8 cm tall .
The layers is done the same way.
However consider that the more layers are added the larger the circumference becomes. there fore I usually calculate the inner and outer layer and then find the average circumference. to be picky one can add that the circumference of the wire is 1 wire radius larger than the core radius. If your even more picky you can calculate the spiral displacement, that is 1 wire diameter for each spiral turn. And even more picky you can try to calculate the coil with the wires into the grooves of the former layer ! ( but that I found out is not really neccesarry) .
Turn Inner Diameter = core diameter + 1 wire diameter = 5cm + 0.511mm * E-1 = 5.0511 cm
Layer Circumference Inner = Pi * Diameter core + Diameter wire = 3.14 * (5cm + 0.511mmE-1) = 15.86 cm
Turn Outer Radius = n layers * Wire diameter = 24 * 0.511mm E-1) = 1.22 cm Radius
Turn Outer Diameter = 1.22 * 2 = 2.45 cm
Layer Circumference Outer = Pi * (D core + Turns outer Diameter) = 3.14 * (5cm + 2.45) = 23.4 cm
The average Circumference will be
O average = Turns Inner Diameter + Turns Outer diameter / 2 = 15.86 + 23.4 / 2 = 19.63 cm long.
To obtain the proper coil one needs to calculate back and forth , and make some coils and test them in a reality check. The first sort of rule of thumb is that the limitations of a coil is the Temprature. The temprature is given by the Ampere in the wire and the coils ability to cool off. A large surface on the coil will cool it off better, like a solenoid. Oils will also cool the coil. If the coil is too hot and the insulation melts, one needs to do either, increase the crossection of the wire, in so doing reducing the resistance, and one needs more turns to obtain the same resistance. Or Increase the resistance with the wire crossection already in use. Iron outside the coil circumference also reduces the Amperes and indirectly cools off the coil. If the coil is cold during operation, you can use a thinner wire or reduce the Resitance. I have a digital temprature or IR meter that gives an indication of the temprature. The other limitation of a coil is in the E-field or static field, Once high voltage is obtained the static will want to arc over the coil turns, particularely where the wires are crossing. and very voulnerable at the IN and OUT wires. that can cross over wires of the coil or parts of ground, inducing an arcing between the turns. Its therefore important to insulate the turns that is crossing the other wires perpendicular, an any axis. The coil and capacitor is therefore a path to master the polar fields of the B-field and E-field. These two fields separate themselvs from the other fields in physics, gravity for instance that may be a monopolar field, Gravity rejects no matter, and has no opposite pole. the electrons alone in a cathode ray also seems like a Monopole field, that attracts and recject the magnetic projection in respective terms. the electron is known for being a "monopole" of a negative charge. the Atom stripped of electrons is said to be of positive charge. together the Atom makes a dipole. If you ever philosopied on "Parallell dimensions" the static and magnetic and gravitational and Temprature are all different fields working at the same time. You dont have to go to outer space to experience a parallell dimension !
A mathematical digression.
When the formulas have certain symbols, they are expressing a specific object. to me it seems all math is based on the 3 basic ground shapes, and a combination of the following. The Square. The Triangle, and the Circle. the symbols applying to them is distinct. when these symbols are used. one can be shure these are the shapes that apples to describe the phenomena.
the Square : Lenghts. Addition, Subtraction, Multiplication and Division. Square root. Area, Cubes and Time.
the Triangle : Cosinus phi, sinius phi for right angled triangles, along with degrees of 180 ( half the degrees of a Square). Kathets and Hypothenus.
the Circle = Pi, radius, diameter. Spheres, Orbits and Fields. When a wheel of 1 lenght diameter rolls one rotation over the ground. The track measures 3.14 in lenght. Magnetic, Static, Tempraure, Light and Gravity fields all tend to be circular from the source, along with waves in water. No matter the shape of the radio antenna, light bulb ( unless it is directional, that limits its broadcast by reflectors or "parasitic elements" like in the Yagi antenna to enhance a desired direction). any wire or coil or even object dropped into water, the waves spread in circles. so they should have the circle symbols in them. I dont know if this is an important question or not but, when is the field so strong that it forms a spherical body around its source . that is how strong must a magnetic field be to form a spheric magnetic field when the source is a cylindrical coil ? how large must the Static field to form a sphere when the plates are an area plate of a certain measure ?
Now that is what I want to say for now.
Hope you enjoy coiling. this is to inspire and share methods of a very interesting topic !
The Coil and Capacitor is practically what runs the "modern society".
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