<p>Some of the comments here seem to be suggesting that there should not be any residual charge of the Sun at all because of the fact that in a conducting medium no electric fields can exist. This argument ignores the crucial point here, namely that there are unequal numbers of positive and negative charges, because electrons, unlike ions, can easily escape from the gravitational field of the sun (in fact, virtually all of them would escape without an electric field holding them back). And any object with an unequal number of positive and negative charges will appear charged from the outside.</p>
<p>The net charge resulting from the escape can easily be calculated from the fact that any particle with a kinetic energy higher than the absolute value of the combined potential energy due to gravity and any net charge <span class="math-container">$Q$</span> inside a sphere of radius <span class="math-container">$R$</span> will escape from the Sun. So for an electron this applies for energies</p>
<p><span class="math-container">$$K_e &gt; \phi_e =\frac{GMm_e+Qe}{R}$$</span></p>
<p>and for ions for energies</p>
<p><span class="math-container">$$K_I &gt; \phi_I = \frac{GMm_I-Qe}{R}$$</span></p>
<p>where <span class="math-container">$G$</span> is the gravitational constant, <span class="math-container">$M$</span> the mass of the sun and <span class="math-container">$e$</span> the absolute value of the elementary charge (using cgs-units here)</p>
<p>In order to achieve a kind of steady state, we must have the same amounts of positive and negative charges escaping, i.e. we must have for the energy distribution functions</p>
<p><span class="math-container">$$f_e(K/\phi_e)=f_I(K/\phi_I)$$</span></p>
<p>where <span class="math-container">$K$</span> is now taken as a general energy variable.</p>
<p>In thermal equilibrium, the distribution functions of the electrons and ion will be the same i.e. <span class="math-container">$f_e=f_I=f$</span> (it should be given by the Maxwell-Boltzmann distribution, but knowing the exact form is not even required here), which means we have the condition <span class="math-container">$\phi_e=\phi_I$</span> (in other words, for electrons and ions of the same kinetic energy to have the same escape rates, they must have the same potential energy) i.e.</p>
<p><span class="math-container">$$GMm_e+Qe = GMm_I-Qe$$</span></p>
<p>and thus</p>
<p><span class="math-container">$$Q=\frac{GM}{2e}(m_I-m_e)$$</span></p>
<p>Inserting the constants for this (with <span class="math-container">$m_I$</span> the proton mass) and converting to SI units gives <span class="math-container">$Q=77$</span> <em>Coulombs</em> for a star the mass of the sun (this value is identical to the one derived in the <a href="https://www.aanda.org/articles/aa/abs/2001/24/aah2649/aah2649.html" rel="nofollow noreferrer">paper by Neslusan</a> (which has already been mentioned a couple of times on SE), but I think my derivation here is more straightforward and easier to understand).</p>
<p>It is remarkable that the charge does <em>only</em> depend on the mass of the star and not for instance on the plasma energy.</p>
<p>For the electric field near the surface of the sun at radius <span class="math-container">$R$</span> we get therefore from Coulomb's law</p>
<p><span class="math-container">$$E=\frac{Q}{R^2} = 1.4\times 10^{-6} \frac{V}{m}$$</span></p>
<p>(after again converting from cgs to SI units).</p>
<p>This electric field is very small. It means that over the size of an atomic orbit the corresponding electric potential energy varies only by about <span class="math-container">$10^{-16} eV$</span>. This would change the wavelength of spectral lines only by an amount which is 12 orders of magnitude smaller than the observed width of spectral lines, so spectroscopically this is impossible to detect.</p>
<p>However,  as you mentioned the solar wind: the fact that this is observed to be quasi-neutral to a high degree shows trivially that the sun must be positively charged by the amount derived above. If the sun would be perfectly neutral there would be a massive excess of electrons in the solar wind (of course, this would then in turn charge up the sun, so  such an assumption would be logically inconsistent in the first place).</p>
<p>It should also be of observable relevance for modelling the solar atmosphere, because the electric field, although very small, effectively halves the gravitational acceleration for ionized atoms, hence resulting in twice the density scale height compared to the neutral atmosphere (a fact that is also well known from observations of the earth's ionosphere).</p>
<p>As far as direct direct experimental verification is concerned, one should not overlook the fact that the electrostatic force on an ion is not only <span class="math-container">$-1/2\times$</span> the gravitational force near the sun (as follows from the above theoretical consideration) but in principle also at any other distance. At the earth, both should be about a factor <span class="math-container">$2\times 10^{-5}$</span> smaller, so the electric field would lead to an acceleration of an ion of about <span class="math-container">$3\times 10^{-4}$</span> the earth's gravitational acceleration of <span class="math-container">$9.81 m/s$</span>. Within a couple of minutes, an ion initially at rest would therefore be accelerated to a speed of the order of <span class="math-container">$1m/s$</span> due to the Sun's charge. The problem will obviously be to eliminate any other electric fields whilst avoiding shielding the field by the experimental setup. I don't know whether this is technically feasible in practice, but in principle it should be possible. Gravimeters are considerably more sensitive than this these days, so at least the effect of both the Earth's and the Sun's gravity could easily be subtracted from the observed acceleration.</p>

CC BY-SA 4.0
2021-07-12T02:31:13.827Z
What is the voltage and capacitance of the Sun? And where do all the electrons go, from all the stars in the universe?
Keith McClary
CC BY-SA 4.0
2021-07-13T21:35:19.030Z
@KeithMcClary The voltage is given by $1/2$ the gravitational potential energy for a proton near the surface of the sun which is about 2 keV, so the sun must at a voltage of +1kV. With a charge of 77 Coulomb, this results in a capacitance of 0.077 farad. The surplus escaped electrons of all the stars will be in interstellar space. It is only a relatively very small amount though, so probably not detectable in practice.
Thomas
CC BY-SA 4.0
2021-07-14T14:56:57.460Z
This just in: [Physicists describe sun's electric field](https://phys.org/news/2021-07-physicists-sun-electric-field.html)
uhoh
CC BY-SA 4.0
2021-07-14T20:09:48.573Z
@uhoh Right on cue then. The paper is not accessible yet though on the ApJ website(the last issue listed there is from July 10). It doesn't seem to be on arXiv either.
Thomas
CC BY-SA 4.0
2021-07-10T21:59:14.163Z
2021-07-14T18:26:27.380Z
2021-07-14T18:26:27.380Z
Thomas
<p>The question <a href="https://astronomy.stackexchange.com/q/23203/7982">Can a Neutron Star become charged?</a> and the associated comments and answers started me wondering; Are there measurements of, or experimental limits to the residual charge of the Sun?</p>

<p>Because the Sun has a complex atmosphere and a net solar wind, I there may be some subtleties related to what sphere is used to establish the net charge Q inside, so rather than me define a radius it may be better to see what evidence is available. </p>

<p>Since there is an ionized component of the solar wind and protons are 2,000 times heavier than electrons, I'm thinking that an initially neutral Sun would loose electrons more rapidly than protons, until a strong enough static field was produced that would add the extra "push" for the protons to leave at the same rate, but that's an extremely simplistic model.</p>

<p>I'm asking primarily for some kind of <strong>measurement or experimental data rather than purely rationalization or hand-waving</strong>. Has there ever been an attempted measurement of the static residual charge of the Sun?</p>

CC BY-SA 3.0
2017-10-28T14:34:24.213Z
Before discarding any rationalizations, you have to realise that any attempt at measuring what you propose will go through rationalizations first. Particularly the rationalization about the size of the Debye-sphere (https://en.wikipedia.org/wiki/Debye_length) of the solar plasma will thwart any thought of doing what you propose in it's infancy.
AtmosphericPrisonEscape
CC BY-SA 3.0
2017-10-28T19:54:49.217Z
@AtmosphericPrisonEscape I didn't propose it, just asked if someone has tried. If you are confident the solar wind can "hide" a net charge on the Sun then why don't you post it as an answer where others can vote on your proposal. Make sure to support your answer with an astronomical reference. Debye length refers to a single charge (e.g. one ion) embedded within an extended plasma *having a substantially larger number of charges*. It only applies when the charge you want to "hide" is much less than the charge available in the plasma. A charge larger than that would not be screened.
uhoh
CC BY-SA 3.0
2017-10-28T20:00:48.090Z
@AtmosphericPrisonEscape also the Debye length applies in a uniform plasma. The density of the solar wind drops as $1/r^2$, it is not at all homogeneous, dropping by over four orders of magnitude by the time it gets to Earth. If you want, I could ask a second question "How much net charge on the sun could be "hidden" by the solar wind?" and you could work it out quantitatively. Let me know!
uhoh
CC BY-SA 3.0
2017-10-28T20:14:44.323Z
@AtmosphericPrisonEscape I just noticed in Physics SE: [What is the electric charge of the Sun and its corona?](https://physics.stackexchange.com/a/73773/83380) It links to [this thread[(http://www.internationalskeptics.com/forums/showpost.php?p=6673481&postcount=947) which cites some calculations by Eddington and therefore a bit dated. But in science, the fact that something has been predicted to be small has never bean a reason to *not bother to measure it*.I'd still like to know if anyone has ever tried to verify a prediction.
uhoh
CC BY-SA 3.0
2017-10-29T14:45:40.063Z
What I was trying to say is the following: When measuring a quantity you use some effect that would make this quantity measurable. Most physics experiments can't measure what they want directly. And the debye length tells you that any an all effects of net charge imbalances in a plasma like the solar wind will be smoothed out on the length scale of ~10 meters. Thus any attempt to measure the suns net charge must fail, as also any plasma intro teaches you.
AtmosphericPrisonEscape
CC BY-SA 3.0
2017-10-29T15:00:47.150Z
@AtmosphericPrisonEscape the idea that an arbitrarily large quantity of charge 10 meters away from you could be completely screened by a rarified plasma with the density of the solar wind at 1 AU does not fly. If you can *quantitatively demonstrate* that a charged Sun is impossible to detect with a modern spacecraft or any other technique, or find a reliable source that does, then post that as an answer. But just saying "There exists a Debye length so your question is moot" in a comment doesn't help, because I don't believe it is necessarily so.
uhoh
CC BY-SA 3.0
2017-10-29T15:04:06.733Z
"...because I don't believe it is necessarily so." Well I think that's more the issue here.
AtmosphericPrisonEscape
CC BY-SA 3.0
2017-10-29T17:23:05.907Z
As I pointed out in the answer on which you commented, electric fields do work to get rid of themselves.  Being that plasmas tend toward quasi-neutrality and any excess charge in the collisional low solar atomosphere will recombine or extinguish itself, the current model (called an exospheric model) is that the sun remains quasi-neutral.  The models that argue it charges up cannot produce a supersonic solar wind, which is constantly observed.  There are some astrophysicists that argue this is valid, but it is just not consistent with observations.
honeste_vivere
CC BY-SA 3.0
2017-10-30T00:58:28.227Z
@honeste_vivere thanks for your comment. If there is some accepted, peer-reviewed work that demonstrates that the presence of a supersonic wind makes a measurement of a residual charge impossible, or a *measurable charge* impossible, that might be a good answer here. Of course a better answer would be "yes there has been a measurement or experimental limit", or "no there hasn't", because I didn't ask if a measurement should or could be made, but instead, asked if one has been.
uhoh
CC BY-SA 3.0
2017-10-30T01:00:00.583Z
@AtmosphericPrisonEscape I don't believe that saying "there exists a Debye length so the question is moot" is correct, and I don't believe the solar wind can mask an arbitrarily large amount of charge in 10 meters. If you can show otherwise, post it as an answer where it can be voted on. Or consider posting an answer to the question as asked.
uhoh
CC BY-SA 3.0
2017-10-30T13:50:55.110Z
@uhoh - Have you looked at the references in this answer https://physics.stackexchange.com/a/257548/59023 ?  Those observations would not be possible, nor would they be made, were the sun allowed to charge up as implied by this answer https://physics.stackexchange.com/a/73773/59023 (Notice that his response to my criticisms in the comments are effectively:  "Just because my model is not supported by observations does not mean it is not valid..." which completely baffles me.).
honeste_vivere
CC BY-SA 3.0
2017-10-30T18:23:12.657Z
@honeste_vivere I hadn't seen that before. OK I'll take a look and give them a read, thanks!
uhoh
CC BY-SA 4.0
2018-11-30T08:23:39.460Z
@honeste_vivere : "Those observations would not be possible, nor would they be made, were the sun allowed to charge up as implied by this answer physics.stackexchange.com/a/73773/59023 " My answer there does not imply that the Sun "charges up", it states (based on a reference) that the Sun has a net charge (these two statements are very different, as the first one means the charge increases). As far as I can see, you did not provide any valid argument against the Sun having a net charge.
akhmeteli
CC BY-SA 4.0
2018-12-04T03:36:33.093Z
@honeste_vivere : "A sun with a net charge as implied by the model you referenced would not allow for a supersonic solar wind, which we constantly observe. I fail to see why that is not a valid argument." Because so far it is baseless. It is just your opinion. Could you support this statement with a decent reference?
akhmeteli
CC BY-SA 4.0
2018-12-04T15:28:51.770Z
@honeste_vivere : I insist that this is irrelevant, because the reference that states there is net charge cannot prove that there is no net charge:-). What we are left with is just your words, which cannot prove that "A sun with a net charge... would not allow for a supersonic solar wind" I just cannot believe you on your words. If some specific model is not perfect, that does not mean that there is no charge. Until you give a decent reference confirming that there is no net charge, your "valid argument" remains baseless, and I reject it.
akhmeteli
CC BY-SA 4.0
2018-12-05T03:42:28.690Z
@honeste_vivere : It is not explained in Lemaire article at all - there is nothing there about net charge of the Sun. It is your responsibility to give a specific quote supporting your opinion if I missed something in the 40-page long article. " I think your adherence to the net charge thing is a red herring because that was not the main issue." I categorically reject this statement. The question at https://physics.stackexchange.com/questions/73763/what-is-the-electric-charge-of-the-sun-and-its-corona is about net electric charge, nothing else. The question here is also about residual charge.
akhmeteli
CC BY-SA 4.0
2018-12-05T03:51:54.143Z
@honeste_vivere : "I do not understand the motivation of your argument or why you defend a model that does not support data." Look, I gave the estimate of the net charge of the Sun from a published article. You don't like the article and the model they use. Very well. Then why don't you give an estimate of the net charge from an article you like? Until you do that, I am happy with the estimate from my answer. Newtonian mechanics is not consistent with data for relativistic velocities, but that does not mean one cannot use it for other purposes.
akhmeteli
CC BY-SA 4.0
2018-12-05T04:15:39.313Z
I am guessing that the **move to chat** option has been offered to each of you by now. This exchange is not really helpful (or interesting) for anyone else to read. Why not move it to a chat room, *delete here*, and when it's resolved just add some kind of conclusion instead; ideally *as an answer to my question*. Comments here should not be used for an extended discussion between two other users, that's what chat is for. Thanks!!
uhoh
CC BY-SA 4.0
2021-03-16T14:48:02.210Z
Which part of the Sun do you want to measure the charge of?
Craeft
CC BY-SA 4.0
2021-03-16T16:06:56.000Z
@Craeft the questions simply asks if any experimental limits exist.
uhoh
<observational-astronomy><the-sun><solar-wind>
What are the experimental limits to the residual charge of the Sun?
uhoh
# What are the experimental limits to the residual charge of the Sun?

(Asked by: username_0 on 2017-10-27)

The question [Can a Neutron Star become charged?](https://astronomy.stackexchange.com/q/23203/7982) and the associated comments and answers started me wondering; Are there measurements of, or experimental limits to the residual charge of the Sun?

Because the Sun has a complex atmosphere and a net solar wind, I there may be some subtleties related to what sphere is used to establish the net charge Q inside, so rather than me define a radius it may be better to see what evidence is available.

Since there is an ionized component of the solar wind and protons are 2,000 times heavier than electrons, I'm thinking that an initially neutral Sun would loose electrons more rapidly than protons, until a strong enough static field was produced that would add the extra "push" for the protons to leave at the same rate, but that's an extremely simplistic model.

I'm asking primarily for some kind of **measurement or experimental data rather than purely rationalization or hand-waving**. Has there ever been an attempted measurement of the static residual charge of the Sun?

**Tags:** observational-astronomy, the-sun, solar-wind
> **Comments:**
> **username_1**: Before discarding any rationalizations, you have to realise that any attempt at measuring what you propose will go through rationalizations first. Particularly the rationalization about the size of the Debye-sphere (https://en.wikipedia.org/wiki/Debye_length) of the solar plasma will thwart any thought of doing what you propose in it's infancy.  
> **username_0**: @AtmosphericPrisonEscape I didn't propose it, just asked if someone has tried. If you are confident the solar wind can "hide" a net charge on the Sun then why don't you post it as an answer where others can vote on your proposal. Make sure to support your answer with an astronomical reference. Debye length refers to a single charge (e.g. one ion) embedded within an extended plasma *having a substantially larger number of charges*. It only applies when the charge you want to "hide" is much less than the charge available in the plasma. A charge larger than that would not be screened.  
> **username_0**: @AtmosphericPrisonEscape also the Debye length applies in a uniform plasma. The density of the solar wind drops as $1/r^2$, it is not at all homogeneous, dropping by over four orders of magnitude by the time it gets to Earth. If you want, I could ask a second question "How much net charge on the sun could be "hidden" by the solar wind?" and you could work it out quantitatively. Let me know!  
> **username_0**: @AtmosphericPrisonEscape I just noticed in Physics SE: [What is the electric charge of the Sun and its corona?](https://physics.stackexchange.com/a/73773/83380) It links to [this thread[(http://www.internationalskeptics.com/forums/showpost.php?p=6673481&postcount=947) which cites some calculations by Eddington and therefore a bit dated. But in science, the fact that something has been predicted to be small has never bean a reason to *not bother to measure it*.I'd still like to know if anyone has ever tried to verify a prediction.  
> **username_1**: What I was trying to say is the following: When measuring a quantity you use some effect that would make this quantity measurable. Most physics experiments can't measure what they want directly. And the debye length tells you that any an all effects of net charge imbalances in a plasma like the solar wind will be smoothed out on the length scale of ~10 meters. Thus any attempt to measure the suns net charge must fail, as also any plasma intro teaches you.  
> **username_0**: @AtmosphericPrisonEscape the idea that an arbitrarily large quantity of charge 10 meters away from you could be completely screened by a rarified plasma with the density of the solar wind at 1 AU does not fly. If you can *quantitatively demonstrate* that a charged Sun is impossible to detect with a modern spacecraft or any other technique, or find a reliable source that does, then post that as an answer. But just saying "There exists a Debye length so your question is moot" in a comment doesn't help, because I don't believe it is necessarily so.  
> **username_1**: "...because I don't believe it is necessarily so." Well I think that's more the issue here.  
> **username_2**: As I pointed out in the answer on which you commented, electric fields do work to get rid of themselves.  Being that plasmas tend toward quasi-neutrality and any excess charge in the collisional low solar atomosphere will recombine or extinguish itself, the current model (called an exospheric model) is that the sun remains quasi-neutral.  The models that argue it charges up cannot produce a supersonic solar wind, which is constantly observed.  There are some astrophysicists that argue this is valid, but it is just not consistent with observations.  
> **username_0**: @honeste_vivere thanks for your comment. If there is some accepted, peer-reviewed work that demonstrates that the presence of a supersonic wind makes a measurement of a residual charge impossible, or a *measurable charge* impossible, that might be a good answer here. Of course a better answer would be "yes there has been a measurement or experimental limit", or "no there hasn't", because I didn't ask if a measurement should or could be made, but instead, asked if one has been.  
> **username_0**: @AtmosphericPrisonEscape I don't believe that saying "there exists a Debye length so the question is moot" is correct, and I don't believe the solar wind can mask an arbitrarily large amount of charge in 10 meters. If you can show otherwise, post it as an answer where it can be voted on. Or consider posting an answer to the question as asked.  
> **username_2**: @uhoh - Have you looked at the references in this answer https://physics.stackexchange.com/a/257548/59023 ?  Those observations would not be possible, nor would they be made, were the sun allowed to charge up as implied by this answer https://physics.stackexchange.com/a/73773/59023 (Notice that his response to my criticisms in the comments are effectively:  "Just because my model is not supported by observations does not mean it is not valid..." which completely baffles me.).  
> **username_0**: @honeste_vivere I hadn't seen that before. OK I'll take a look and give them a read, thanks!  
> **username_3**: @honeste_vivere : "Those observations would not be possible, nor would they be made, were the sun allowed to charge up as implied by this answer physics.stackexchange.com/a/73773/59023 " My answer there does not imply that the Sun "charges up", it states (based on a reference) that the Sun has a net charge (these two statements are very different, as the first one means the charge increases). As far as I can see, you did not provide any valid argument against the Sun having a net charge.  
> **username_3**: @honeste_vivere : "A sun with a net charge as implied by the model you referenced would not allow for a supersonic solar wind, which we constantly observe. I fail to see why that is not a valid argument." Because so far it is baseless. It is just your opinion. Could you support this statement with a decent reference?  
> **username_3**: @honeste_vivere : I insist that this is irrelevant, because the reference that states there is net charge cannot prove that there is no net charge:-). What we are left with is just your words, which cannot prove that "A sun with a net charge... would not allow for a supersonic solar wind" I just cannot believe you on your words. If some specific model is not perfect, that does not mean that there is no charge. Until you give a decent reference confirming that there is no net charge, your "valid argument" remains baseless, and I reject it.  
> **username_3**: @honeste_vivere : It is not explained in Lemaire article at all - there is nothing there about net charge of the Sun. It is your responsibility to give a specific quote supporting your opinion if I missed something in the 40-page long article. " I think your adherence to the net charge thing is a red herring because that was not the main issue." I categorically reject this statement. The question at https://physics.stackexchange.com/questions/73763/what-is-the-electric-charge-of-the-sun-and-its-corona is about net electric charge, nothing else. The question here is also about residual charge.  
> **username_3**: @honeste_vivere : "I do not understand the motivation of your argument or why you defend a model that does not support data." Look, I gave the estimate of the net charge of the Sun from a published article. You don't like the article and the model they use. Very well. Then why don't you give an estimate of the net charge from an article you like? Until you do that, I am happy with the estimate from my answer. Newtonian mechanics is not consistent with data for relativistic velocities, but that does not mean one cannot use it for other purposes.  
> **username_0**: I am guessing that the **move to chat** option has been offered to each of you by now. This exchange is not really helpful (or interesting) for anyone else to read. Why not move it to a chat room, *delete here*, and when it's resolved just add some kind of conclusion instead; ideally *as an answer to my question*. Comments here should not be used for an extended discussion between two other users, that's what chat is for. Thanks!!  
> **username_4**: Which part of the Sun do you want to measure the charge of?  
> **username_0**: @Craeft the questions simply asks if any experimental limits exist.  

---

## 1 answers

### Answer by username_5 on 2021-07-10. Score: 8 | Accepted answer

Some of the comments here seem to be suggesting that there should not be any residual charge of the Sun at all because of the fact that in a conducting medium no electric fields can exist. This argument ignores the crucial point here, namely that there are unequal numbers of positive and negative charges, because electrons, unlike ions, can easily escape from the gravitational field of the sun (in fact, virtually all of them would escape without an electric field holding them back). And any object with an unequal number of positive and negative charges will appear charged from the outside.

The net charge resulting from the escape can easily be calculated from the fact that any particle with a kinetic energy higher than the absolute value of the combined potential energy due to gravity and any net charge $Q$ inside a sphere of radius $R$ will escape from the Sun. So for an electron this applies for energies

$$K\_e > \phi\_e =\frac{GMm\_e+Qe}{R}$$

and for ions for energies

$$K\_I > \phi\_I = \frac{GMm\_I-Qe}{R}$$

where $G$ is the gravitational constant, $M$ the mass of the sun and $e$ the absolute value of the elementary charge (using cgs-units here)

In order to achieve a kind of steady state, we must have the same amounts of positive and negative charges escaping, i.e. we must have for the energy distribution functions

$$f\_e(K/\phi\_e)=f\_I(K/\phi\_I)$$

where $K$ is now taken as a general energy variable.

In thermal equilibrium, the distribution functions of the electrons and ion will be the same i.e. $f\_e=f\_I=f$ (it should be given by the Maxwell-Boltzmann distribution, but knowing the exact form is not even required here), which means we have the condition $\phi\_e=\phi\_I$ (in other words, for electrons and ions of the same kinetic energy to have the same escape rates, they must have the same potential energy) i.e.

$$GMm\_e+Qe = GMm\_I-Qe$$

and thus

$$Q=\frac{GM}{2e}(m\_I-m\_e)$$

Inserting the constants for this (with $m\_I$ the proton mass) and converting to SI units gives $Q=77$ *Coulombs* for a star the mass of the sun (this value is identical to the one derived in the [paper by Neslusan](https://www.aanda.org/articles/aa/abs/2001/24/aah2649/aah2649.html) (which has already been mentioned a couple of times on SE), but I think my derivation here is more straightforward and easier to understand).

It is remarkable that the charge does *only* depend on the mass of the star and not for instance on the plasma energy.

For the electric field near the surface of the sun at radius $R$ we get therefore from Coulomb's law

$$E=\frac{Q}{R^2} = 1.4\times 10^{-6} \frac{V}{m}$$

(after again converting from cgs to SI units).

This electric field is very small. It means that over the size of an atomic orbit the corresponding electric potential energy varies only by about $10^{-16} eV$. This would change the wavelength of spectral lines only by an amount which is 12 orders of magnitude smaller than the observed width of spectral lines, so spectroscopically this is impossible to detect.

However, as you mentioned the solar wind: the fact that this is observed to be quasi-neutral to a high degree shows trivially that the sun must be positively charged by the amount derived above. If the sun would be perfectly neutral there would be a massive excess of electrons in the solar wind (of course, this would then in turn charge up the sun, so such an assumption would be logically inconsistent in the first place).

It should also be of observable relevance for modelling the solar atmosphere, because the electric field, although very small, effectively halves the gravitational acceleration for ionized atoms, hence resulting in twice the density scale height compared to the neutral atmosphere (a fact that is also well known from observations of the earth's ionosphere).

As far as direct direct experimental verification is concerned, one should not overlook the fact that the electrostatic force on an ion is not only $-1/2\times$ the gravitational force near the sun (as follows from the above theoretical consideration) but in principle also at any other distance. At the earth, both should be about a factor $2\times 10^{-5}$ smaller, so the electric field would lead to an acceleration of an ion of about $3\times 10^{-4}$ the earth's gravitational acceleration of $9.81 m/s$. Within a couple of minutes, an ion initially at rest would therefore be accelerated to a speed of the order of $1m/s$ due to the Sun's charge. The problem will obviously be to eliminate any other electric fields whilst avoiding shielding the field by the experimental setup. I don't know whether this is technically feasible in practice, but in principle it should be possible. Gravimeters are considerably more sensitive than this these days, so at least the effect of both the Earth's and the Sun's gravity could easily be subtracted from the observed acceleration.

> **Comments:**
> **username_6**: What is the voltage and capacitance of the Sun? And where do all the electrons go, from all the stars in the universe?  
> **username_5**: @KeithMcClary The voltage is given by $1/2$ the gravitational potential energy for a proton near the surface of the sun which is about 2 keV, so the sun must at a voltage of +1kV. With a charge of 77 Coulomb, this results in a capacitance of 0.077 farad. The surplus escaped electrons of all the stars will be in interstellar space. It is only a relatively very small amount though, so probably not detectable in practice.  
> **username_0**: This just in: [Physicists describe sun's electric field](https://phys.org/news/2021-07-physicists-sun-electric-field.html)  
> **username_5**: @uhoh Right on cue then. The paper is not accessible yet though on the ApJ website(the last issue listed there is from July 10). It doesn't seem to be on arXiv either.  

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