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What is the highest electric field known in nature?

To add clarity, as requested: an electric field is measured in V/m, Volt per meter.

What is highest value that has been measured or observed?

What is the highest value that is suspected?

There are two candidates situations and systems where one can search.

(1) Microscopic: Maybe the highest electric field is that found inside hadrons, where the distances are about 1 fm? How large can the electric field be inside them?

(2) Astrophysical: Maybe the highest electric field is in charged black holes, magnetars, neutron stars etc.? How large can the electric field be in those cases?

One reason for the question is the following. The Planck speed is $c$. Accelerators get really close to it, up to over 99.999% of the maximum value. Now, the Planck electric field is $$E_{Planck}=\frac{c^4}{Ge}\ \ \ ,$$ around $10^{63}$ V/m. But the highest electric field value in a microscopic system that I found is around $10^{12}$ V/m (estimate for the field inside an atom). Why is the difference between the highest measured fields to the Planck field so large, in contrast to the situation for speed?

One reason could be that other systems with much higher field values exist that are usually forgotten. Another reason is spontaneous pair creation of electrons and positrons; the effect also limits electric fields.

So far, the highest electric field value in a macroscopic system might be a calculated value in magnetars. Magnetars have magnetic fields up to $10^{11}$ T, which would correspond, using $E=cB$, to about $10^{19}$ V/m.

Do higher electric field values exist in other systems in nature?

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P.S. Google Scholar does not help. Neither does Wikipedia. Searching for "largest electric field" or for "highest electric field" or for "record electric field" gives only relatively small values.

P.P.S. The question "What is the highest electric field known?" seems simple and clear. All details have been given. Maybe it will be reopened one day.

P.P.P.S. If the question is reopened, I will offer a bounty for the answer.

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  • $\begingroup$ I guess that the field inside a meson has a much higher value; around 10^7 times more ... $\endgroup$
    – user85598
    Aug 1, 2020 at 14:23
  • $\begingroup$ how do you define the electric field in a meson? $\endgroup$
    – trula
    Aug 1, 2020 at 14:47
  • $\begingroup$ The electric field is E=F/q $\endgroup$
    – user85598
    Aug 1, 2020 at 19:04
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    $\begingroup$ I've estimated field achievable for a focused 100 TW laser - and it's mere 8.6E10 V/m. So apparently we'll have to deal with subatomic and stellar effects in this question. $\endgroup$
    – BarsMonster
    Dec 1, 2021 at 5:33
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    $\begingroup$ Here's a nice page on Wikipedia with references showing examples of the weakest to strongest magnetic fields. en.wikipedia.org/wiki/Orders_of_magnitude_(magnetic_field) $\endgroup$
    – James
    Dec 1, 2021 at 16:03

2 Answers 2

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Large electric fields produce electron-positron pairs via what's known as the Schwinger effect. When the electric field is large enough, close to the Schwinger limit $10^{18}$ V/m, pair production drains energy from the field, hence decreasing it. Electric fields larger than the Schwinger limit are unstable in nature as they would "decay" to charged pairs. In the lab, one might be able to produce larger electric fields for a short time. Theoretically, fields in the lab can reach the value of a Plank electric field, but to do so one must keep feeding energy into the system at an ever-increasing rate.

https://en.wikipedia.org/wiki/Schwinger_effect https://en.wikipedia.org/wiki/Schwinger_limit

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  • $\begingroup$ Are there any known celestial objects or subatomic particles that can generate electric fields close to the Schwinger limit? $\endgroup$
    – David White
    Oct 27, 2021 at 0:00
  • $\begingroup$ For celestial objects, check out neutron stars. In theory, the electric field of a charged particle such as the electron grows like 1/r^2. r is the distance from the electron. If you go arbitrarily close to the electron you can get an arbitrarily large electric field. E = k e/r^2. In SI units k ~ 10^10, e ~ 10^-19, and to get E ~ 10^18 (the Schwinger limit) you need r ~ 10^-14 m. Still macroscopic compared to the Planck scale. On this scale, virtual particles will be involved. They absorb energy from the field in a manner similar to the Schwinger effect, then they give it back. $\endgroup$
    – Osama Karkout
    Oct 28, 2021 at 9:57
  • $\begingroup$ @OsamaKarkout you have to also take magnetars in consideration $\endgroup$
    – user318515
    Dec 5, 2021 at 10:45
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The Plank electric field value is partly a random mathematical construct, and not necessarily based on any physical reality.

The electron-positron pair production is mentioned earlier, and there are a lot of other limitations for macroscopic E fields before that.

Some examples:

  • The national ignition facility focuses 500TW of laser light onto a 2mm ball.
  • Fiber lasers can carry up to about 200kW with a diameter of 9µm

Field strength of EM radiation $E_0=\sqrt{2I/cε_0}$ so the fiber laser has E fields of 2.2TV/m

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