estimating voltage in earth's core ?

[Widdekind]

Employing the formula for a dipole magnetic field, the field strength, at the surface, at earth's equator is:

[math]B = \frac{1}{4 \pi \epsilon_0 c^2} \frac{m}{R_{\oplus}^3}[/math]

 

[math]m = I A = \left( \mu R_{core} \omega \right) \left( \pi R_{core}^2 \right)[/math]

where i have assumed, that the charge carriers generating the field, reside in earth's metallic core, near the surface of the same, in a toroidal belt about the equator of the same, carrying a charge per unit length of [math]

\mu[/math] (see below). Ergo

[math]B = \frac{\mu \omega}{4 \epsilon_0 c^2} \left( \frac{R_{core}}{R_{\oplus}} \right)^3[/math]

Now, by simple integration, the voltage generated, by a current loop, at the center of the circle, is:

[math]V = \int_0^{2 \pi} \frac{\mu R d \theta}{4 \pi \epsilon_0 R} = \frac{\mu}{2 \epsilon_0}[/math]

Ergo,

[math]V = 2 B \omega c^2 \left( \frac{R_{core}}{R_{\oplus}} \right)^{-3} \approx 10^{10} V[/math]

 

[math]Q = 2 \pi R_{core} \mu = \left(8 \pi^2 \epsilon_0 c^2 \right) \frac{B}{\omega} \left( \frac{R_{core}}{R_{\oplus}} \right)^{-3} R_{core}[/math]

[math]= \left(4 \pi \epsilon_0 c^2 \right) \left(B P \right) \left( \frac{R_{core}}{R_{\oplus}} \right)^{-3} R_{core} \approx 10^{15} C[/math]

According to this model, earth's dynamo is generated by a quintillion Coulombs of charge, generating ten gigavolts, from surface to center of earth's core.

 

If charges were separated, into (say) electrons in an equatorial toroidal belt; and holes in the center; then that configuration would be stable. For, the electrons in the outer belt would generate a dipole magnetic field, which would push them outwards, keeping them in place; whilst holes, experiencing oppositely directed magnetic forces, would be pushed back towards the center, keeping them in place. Only if the field got twisted and "fouled up", would charge carriers begin to migrate out of position. But charge separation would be the stable condition. Charge reversals, brought about by turbulence, field failure, and field re-generation, back into the "other" (charge-reversed) stable condition, could account for random field reversals.

 

Repeating these calculations, for our Sun, would plausibly generate even larger numbers. Approximately, the Sun's rotation period (P) is ~30x longer; and the Sun's core radius is ~30x larger (and is only about ~1/4^th of the Solar radius, instead of ~1/2 as for Earth). Those numbers would reduce the Sun's core voltage, compared to Earth, by a factor of a few (few GV); but increase the charge separation by a factor of 10⁴ (10¹⁹ C).

Edited October 1, 2012 by Widdekind

[swansont]

AFAIK the model is that the current is generated form the motion of the core, not a potential disfference. Even if it were a potential, it would be around the current path (which is how you know it's not caused by a potential), not between the core and the surface.

[Ronald Hyde]

This is very important to me. I've long ago rejected the 'motion of the Earth's core' hypothesis as it is completely ad hoc

and without any kind of observational support. I know how dynamos work, and they need to be carefully designed to work at all.

I've looked at the 'other way' of making magnetic fields, spontaneous

symmetry breaking, aka ferromagnetism but haven't come up with anything.

 

More stuff to include in your theorizing. It's long known that the Sun has a quadrupole field, it's part of the Solar Cycle,

now it's being found out that the Earth has one too. Do all large rotating bodies? Another big question. How do the magnetic

fields associated with the Van Allen belts arise? The belts are practically defined by these fields, if the fields disappeared so

would the belts. And of course other planets have these toroidal 'belts'.

 

My intuition say that you might be on to something. I'm wondering how those equations were arrived that, very much so.

[Widdekind]

Iron can have magnetization densities of [math]\leq 10^6 A/m[/math]. Ergo, the magnetic moment in earth's core could derive from the spin-magnetic moments, of the vast masses of iron atoms, residing therein:

[math]B \cong \frac{\mu_0}{4 \pi} \frac{M}{R_{\oplus}^3}[/math]

 

[math]M \cong \frac{4 \pi}{\mu_0} R_{\oplus}^3 B[/math]

 

[math]m \cong \frac{M}{\left( \frac{4 \pi R_{core}^3}{3} \right)}[/math]

[math]= \frac{3 B}{\mu_0} \left( \frac{R_{\oplus}}{R_{core}} \right)^3 [/math]

[math]\approx 10^3 A/m[/math]

---

The OP proposed that charges are separated, in earth's core, with (say) electrons residing in a negatively-charged toroidal belt about the equator of the core; and with (say) holes residing on the rotation axis. That proposed configuration would resemble the 'dz2' electron orbital:

The outer belt of (say) electrons would generate a magnetic field, which would tend to keep the electrons away from the central axis; and which would tend to keep the holes on the axis. Thus, the configuration would be magnetically stable. But, there would be a strong electrical attraction, between the regions of opposite electric charge. Without finagling the numbers, the electrical attraction would be (?) three orders of magnitude greater than the magnetic repulsion. The numbers work out much better for stars, which are larger, and can keep the charges farther apart. Perhaps stars may generate dynamos electrically; but perhaps worlds, composed of non-ionized material, generate dynamos magnetically??

---

The magnetic potential energy of earth's core is small, compared to the gravitational potential energy, of earth:

[math]B_{core} \cong \frac{\mu_0}{4 \pi} \frac{M}{R_{core}^3} = B_{\oplus} \times \left( \frac{R_{\oplus}}{R_{core}} \right)^3[/math]

 

[math]M \cong \frac{4 \pi}{\mu_0} R_{\oplus}^3 B_{\oplus}[/math]

 

[math]U = - M B_{core} = - M B_{\oplus} \times \left( \frac{R_{\oplus}}{R_{core}} \right)^3[/math]

[math]= - \left( \frac{4 \pi R_{\oplus}^3}{3} \right) \left( \frac{3 B^2}{\mu_0} \right) \left( \frac{R_{\oplus}}{R_{core}} \right)^3[/math]

[math]\approx - 10^{20} J[/math]

For comparison,

[math]U_G \approx - \frac{3}{5} \frac{G M_{\oplus}^2}{R_{\oplus}} \approx - 10^{32} J[/math]

Earth's internal natural nuclear fission geo-reactor generates ~45TW of power; the magnetic potential energy of earth's core is about one "earth month" of energy; the world's gravitational potential energy is about a trillion times more, or about a hundred billion "world years" of energy.

[Ronald Hyde]

I see that you have more, and are doing very well with connecting with observables. I have more too, but it connects with things that happen above the Earths surface

and are more observable. What I am dealing with tells me that around every large body there are layers and boundaries between them. At first I called these abstract

layers, but then it began to dawn that these were real physical layers, and for the Earth and the Sun they had already been given names. So I could understand why

and how things were happening, lightning and such, and even write a few equations myself. But it's getting very hot where I am, I will come back when things are

cooler and write much more.

 

Isn't it nice to know that someone understands what you are saying when you talk about something new?

Another 'out of the box' thinker.

[T L E]

Hmmmm...if I place an 'electrode' (say a metal bar 1-foot long) in a deep mine and run a wire from the 'bar' to the surface, would I be able to detect a current from the end of that wire and another 'bar' touching the surface/ground ? And, if so, would the current strength increase/vary the deeper the mine 'bar' is placed below the surface? ...And would it work better if the 'bars' were, say, copper for one bar and iron for the other....? (Trivia: You can detect a current between a brass nail and an iron nail driven, say, 2-inches apart AND 3-inches deep into a maple tree -- the only tree I tried.... [Hmm, try this with a forest and wire 'them' in series/parallel......................]) ;0

 

T L E

Edited October 1, 2012 by T L E

[Ronald Hyde]

Hmmmm...if I place an 'electrode' (say a metal bar 1-foot long) in a deep mine and run a wire from the 'bar' to the surface, would I be able to detect a current from the end of that wire and another 'bar' touching the surface/ground ? And, if so, would the current strength increase/vary the deeper the mine 'bar' is placed below the surface? ...And would it work better if the 'bars' were, say, copper for one bar and iron for the other....? (Trivia: You can detect a current between a brass nail and an iron nail driven, say, 2-inches apart AND 3-inches deep into a maple tree -- the only tree I tried.... [Hmm, try this with a forest and wire 'them' in series/parallel......................]) ;0

 

T L E

 

I don't know about your particular problem, but near the Earths surface, in the air, there is a constant potential gradient of about 300V/Meter and a constant current

associated with it. If you integrate this current over the Earths surface it neatly cancels out the currents associated with Lightning.

 

I'm going to start adding stuff. This may be somewhat rambling but it's all connected together, I can't explain everything all at once in this post and don't intend to try.

Some of it connects directly with Weddekind's posts, some is a bit aside from it.

 

This concerns Self Organizing Systems, the Universe as a self organizing system, organizing principles, but that's a much larger topic and I'm

not going into detail on that. If you look up 'self organizing systems' in Wikipedia you will find that it is a large well developed field.

 

To Weddekind I'm going to say that the processes you describe may be what I call 'entropically driven' processes, the total energy

remains the same but the entropy is continually pushed in the negative direction, so that the process is maintained. This violates one

or more of the 'laws of thermodynamics' but it only works on the larger scale so you won't be able to get work out of it.

 

The layers, Earth layers. Names like Troposphere, Ionosphere, etc., some of these are layers, others like the Ozone Layer, are thin boundaries

between layers. The Sun has its own layers and boundaries and they are well observed.

 

I'm only going to describe things close to the Earth's surface, as they are easy to observe and related to Weddekind's posts.

I've spent more than a few lazy afternoons watching thunderstorms develop. Where I live now they rarely happen and mostly at night, so

I can't do that anymore. What I saw was first a few white puffy clouds forming at a specific height above Earth. Soon one cloud would begin

growing in width and later in height. It would no longer be pure white, would take on darker hues, get that 'silver lining'. I now know that

the cloud is sitting on top of a boundary, and as it grows upward it reaches another boundary, and starts spreading out at the top. It forms

the characteristic 'anvil shape' of thunderstorms. Here is where the fun begins. The topmost boundary and the Earth's surface form a giant

electrical capacitor, with an enormous charge and a huge potential drop between them, I've read something like a hundred million volts.

 

The thundercloud partly short-circuits the capacitor, so the air near the bottom of the cloud starts to break down, and sends a 'step leader'

toward ground. The step leader is tree like with many branches, which ever branch touches a good conductor from ground starts a return

stroke, which is the lightning that we see. I used to believe that the lightning was caused by a Van de Graff generator effect in the cloud, I'm

beginning to think that more is involved. The charge at the topmost boundary may be related to the charge in Weddekind's post.

 

Where Q is the charge difference between two concentric conducting spheres:

 

Total energy: [latex] Q^2 2 \pi / r_1 + r_2 [/latex]

Potential is that divided by Q/2

 

where the two r's are the radii.

 

Enough for now.

[Widdekind]

Geologically, earth is a big rubble-pile of rock in space. Earth has a macroscopic dipolar field; earth is composed largely of iron; iron atoms have microscopic dipolar fields. Parsimoniously, earth's core generates a big dipole field, by the combined efforts, of zillions of iron atoms.

 

Stars, by contrast, generate more complex fields; perhaps theirs derive from electrical currents?

 

Again, earth is composed of non-ionic material; non-ionic material generates magnetic fields, from intrinsic quantum dipole moments. All natural magnets known are such. Perhaps earth is "just a big lump of lodestone"? Perhaps the core is a giant ferromagnet, undergoing zone growths, and decays, and thermal heat destabilizes some zones, which then re-establish themselves, only to decay again later... every so often, the entire core is thermally de-magnetized, and it takes awhile for core-sized zones to regrow??

[sammy7]

http://www.icr.org/i...etic-Fields.pdf

 

 

In 1983, on the basis of Scriptures implying the original created material of the earth was water,

I proposed that God created the water with the spins of its hydrogen nuclei initially aligned in one

direction (Humphreys, 1983). That would produce a strong magnetic field. After 6,000 years of decay,

including energy losses from magnetic reversals during the Genesis Flood, (Humphreys, 1986a, 1990c)

the strength of the earth's magnetic field would be what we observe today. In 1984 I extended the

theory to the other planets of the solar system, the Sun, and the Moon (Humphreys, 1984). The theory

explained the observed magnetic field strengths of those bodies very well. It also correctly predicted

the field strengths of Uranus and Neptune measured by the Voyager 2 spacecraft several years later,

(Humphreys, 1986b, 1990a, b) as well as magnetizations of surface rocks on Mars (Humphreys, 1999).

In this paper I improve the theory and apply it to updated solar system data, meteorites, and the

larger moons of Jupiter and Saturn. Then in a brief survey I apply it beyond our solar system to ordinary

stars, magnetic stars, white dwarf stars, pulsars, "magnetars," galaxies, and the cosmos itself. The

theory appears to be able to explain the magnetic fields of all heavenly bodies for which we have

magnetic data. In contrast, the origin of cosmic magnetic fields is still a great mystery to uniformitarian

theorists (Langer, Puget, & Aghanim, 2003).

Edited October 6, 2012 by sammy7

[John Cuthber]

http://www.icr.org/i...etic-Fields.pdf

 

 

In 1983, on the basis of Scriptures implying the original created material of the earth was water,

I proposed that God created the water with the spins of its hydrogen nuclei initially aligned in one

direction (Humphreys, 1983).

 

LOL

Sammy,

This is a science forum.

You can't cite fairy tales as evidence.

[swansont]

Geologically, earth is a big rubble-pile of rock in space. Earth has a macroscopic dipolar field; earth is composed largely of iron; iron atoms have microscopic dipolar fields. Parsimoniously, earth's core generates a big dipole field, by the combined efforts, of zillions of iron atoms.

 

Stars, by contrast, generate more complex fields; perhaps theirs derive from electrical currents?

 

Again, earth is composed of non-ionic material; non-ionic material generates magnetic fields, from intrinsic quantum dipole moments. All natural magnets known are such. Perhaps earth is "just a big lump of lodestone"? Perhaps the core is a giant ferromagnet, undergoing zone growths, and decays, and thermal heat destabilizes some zones, which then re-establish themselves, only to decay again later... every so often, the entire core is thermally de-magnetized, and it takes awhile for core-sized zones to regrow??

The earth's field periodically reverses itself, which isn't something a big lump of lodestone does.

[Ronald Hyde]

Geologically, earth is a big rubble-pile of rock in space. Earth has a macroscopic dipolar field; earth is composed largely of iron; iron atoms have microscopic dipolar fields. Parsimoniously, earth's core generates a big dipole field, by the combined efforts, of zillions of iron atoms.

 

Stars, by contrast, generate more complex fields; perhaps theirs derive from electrical currents?

 

Again, earth is composed of non-ionic material; non-ionic material generates magnetic fields, from intrinsic quantum dipole moments. All natural magnets known are such. Perhaps earth is "just a big lump of lodestone"? Perhaps the core is a giant ferromagnet, undergoing zone growths, and decays, and thermal heat destabilizes some zones, which then re-establish themselves, only to decay again later... every so often, the entire core is thermally de-magnetized, and it takes awhile for core-sized zones to regrow??

I'm thinking that your speculations about the currents in your first posts is more in line with the physical reality, that some as yet unknown mechanism drives the currents

and the currents involved in the atmosphere in my thundercloud description, and also don't forget the quadrupole aspect. And the Sun has the same kinds of fields and

the same sort of periodicity, except more often and regularly. And that periodicity is tied to the Solar Cycle and the huge body of unexplained physics known as Solar Activity.

In the past couple of decades much effort has been put into the Solar field, experimentally starting with the T.R.A.C.E. satellite and recently its successor the SDO, plus other

satellites and instruments. But most anyone will tell you that there is no competent theory of how Solar Activity works, none. So this is a field that is very ripe for

theoretical development.

[Phi for All]

http://www.icr.org/i...etic-Fields.pdf

 

 

In 1983, on the basis of Scriptures implying the original created material of the earth was water,

I proposed that God created the water with the spins of its hydrogen nuclei initially aligned in one

direction (Humphreys, 1983). That would produce a strong magnetic field. After 6,000 years of decay,

including energy losses from magnetic reversals during the Genesis Flood, (Humphreys, 1986a, 1990c)

the strength of the earth's magnetic field would be what we observe today. In 1984 I extended the

theory to the other planets of the solar system, the Sun, and the Moon (Humphreys, 1984). The theory

explained the observed magnetic field strengths of those bodies very well. It also correctly predicted

the field strengths of Uranus and Neptune measured by the Voyager 2 spacecraft several years later,

(Humphreys, 1986b, 1990a, b) as well as magnetizations of surface rocks on Mars (Humphreys, 1999).

In this paper I improve the theory and apply it to updated solar system data, meteorites, and the

larger moons of Jupiter and Saturn. Then in a brief survey I apply it beyond our solar system to ordinary

stars, magnetic stars, white dwarf stars, pulsars, "magnetars," galaxies, and the cosmos itself. The

theory appears to be able to explain the magnetic fields of all heavenly bodies for which we have

magnetic data. In contrast, the origin of cosmic magnetic fields is still a great mystery to uniformitarian

theorists (Langer, Puget, & Aghanim, 2003).

!

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