Is there a maximum strength for an electric field pressure?

[Crazymechanic]

Now I'm not exactly sure if someone hasn't asked a question like this, probably it has been done but I haven't stumbled upon one yet.

Does the electric field has an upper limit of strength (force) it exerts on a mixture of gas for example or any other particle /fluid or gas or solid which interacts with it?

Or in other words if I have a metal plate in a vacuum at some given potential that keeps on rising higher every second , can this go on forever and the field get ever stronger with increasing voltage? Is there an upper limit , even a theoretical one?
Theoretically , ignoring that on daily conditions it would make an electric breakdown of surrounding matter etc etc.

 

[Jolb]

Well in classical E&M, there is no upper limit.

In real life, though, in your thought experiment where you have a plate whose voltage constantly increases, then eventually what would happen is that the field would pull apart virtual particle-antiparticle pairs. The "vacuum polarization" would eventually become relevant and you could start pulling electrons and positrons (and other particle-antiparticle pairs) out of the vacuum.

If you had a gas in the field, eventually the field would ionize the gas into its constituent charged particles and rip the gas apart. This would probably happen at a much lower energy than the vacuum polarization issue.

You would also have to worry about the plate discharging. If there were two plates, then you might get some arc traveling between the two plates (this can happen in vacuum and depends on the fermi surface).

 

[Crazymechanic]

Ok, if we forget about the plate discharging through some path and etc , does the vacuum polarization decreases the strength of the electric field which is due to the potential (voltage) on the plate ? And if so is it because the energy goes into creating these pairs?
Also what happens when these pairs are created as I understand they are "virtual" aka short living particles and when they annihilate do they increase the E field or what , as energy has to be conserved I guess they are either decreasing the potential on the plate and contributing to the E field or something?

I really cold have find answers to these questions myself but seems that vacuum polarization is not the most talked about topic around.

 

[Jolb]

Here's a reference from none other than Heisenberg himself:
http://arxiv.org/abs/physics/0605038

And a more modern one:
http://arxiv.org/abs/1112.4120

does the vacuum polarization decreases the strength of the electric field which is due to the potential (voltage) on the plate ? And if so is it because the energy goes into creating these pairs?

Yes; in order to create these electron-positron pairs, work must be done by the field of the plate, so pair production does leech energy from the plates. Even without pulling apart the pairs, the virtual electron-positron pairs act like a dielectric medium, so they always reduce the field strength.

Moreover, once the charges are pulled apart, they'll be attracted to the oppositely-charged plates and cancel out some of the charge on the plates.

Also what happens when these pairs are created as I understand they are "virtual" aka short living particles and when they annihilate do they increase the E field or what , as energy has to be conserved I guess they are either decreasing the potential on the plate and contributing to the E field or something?

Well, once you pull the pair apart, they stop being "virtual" and become normal "real" particles. To use accurate terminology, this process creates real particles and antiparticles from the virtual pairs; these pairs are always lurking. [This is almost analogous to Hawking radiation.] Once the particles are real, they don't necessarily have to annihilate one another--they can do what I said above and travel to the oppositely charged plate, canceling any accumulated charge.

For the example of your thought experiment, say we had a plate hooked up to the + terminal of a ridiculously strong battery, and for the sake of argument let's say the - terminal is connected by a wire to infinity [maybe there's a plate at infinity too]. Then the plate would continue to charge until the field becomes strong enough to start pair production, then once electrons and positrons start popping into the picture, the positrons would fly away from the + plate off to infinity while the electrons would be drawn to the + plate and neutralize its charge. If we imagine the positrons are flying to the - plate at infinity, the net result is a current from positive to negative, where the circuit is completed by the channel of flying electrons and positrons--this current would run until it wears down the battery.

 

[sardar]

I can confirm that there is no maximum strength for an electric field pressure. The strength of an electric field is determined by the charge and distance between two objects. As long as these factors continue to increase, the electric field strength will also increase.

However, there are practical limitations to the strength of an electric field. As mentioned, at high enough field strengths, the surrounding matter can experience an electric breakdown, which can damage or destroy the objects in the vicinity. Additionally, the laws of thermodynamics dictate that energy cannot be created or destroyed, so there must be a limit to how much energy can be contained within an electric field.

Furthermore, in the scenario described with a metal plate in a vacuum, the electric field strength can continue to increase as long as the voltage is increasing. However, this is not a sustainable or stable system as the metal plate will eventually reach a point where it cannot hold any more charge and the system will reach equilibrium.

In conclusion, while there is no theoretical maximum strength for an electric field pressure, there are practical limitations and considerations that must be taken into account. Further research and experimentation is needed to fully understand the capabilities and limitations of electric fields.