# Why don't charges fly off a conductor?

To be concrete, consider two parallel conducting plates, one positively charged and the other negatively charged. Why doesn't the electric field between the two plates pull the charges off the surface of the two plates?

Matterwave
Gold Member
They can if the voltage is strong enough. If the voltage exceeds the breakdown voltage of the dielectric in between the two plates, you will get arcing of electrons. This is basically what happens during a lightning storm, or when you see sparks fly.

But if the voltage is not strong enough, the insulating material between the plates will prevent the electrons from moving from one plate to the other.

But if the voltage is not strong enough, the insulating material between the plates will prevent the electrons from moving from one plate to the other.

Let's say that the gap between the two plates is a pure vacuum. What's stopping an electron on the surface on the negatively charged conductor from accelerating towards the other conductor?

Matterwave
Gold Member
The electrons are still bound to the protons in the conducting material. They are in the conduction band, but they are still in a bound state. To move them to the other plate, you'd have to take them out of that bound state. Just because you have a conductor doesn't mean you have free electrons that are free to move as they wish.

Remember that electricity is moving electrons, but the electrons usually have to have a path to move through. In a conductor, they move along the conduction band (not out of it). In an insulator that has broken down, they move along the filaments of plasma. In a vacuum, you'd have to really just strip those electrons off the conductor and move them. With a strong enough electric field, I'm sure you can do that. But I don't know how strong of an electric field you would need. My intuition tells me the field must be very strong indeed.

The electric field, classically, of a proton at the typical separation distance of an electron (estimated 1 anstrom) is something like 10^11 N/C (N/C=V/m) so that should give you some indication of perhaps the numbers that are involved. Of course, quantum mechanics will obviously come into play here.

For comparison, the breakdown voltage of air is only 3,000,000 V/m.

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nsaspook
It takes a large field gradient to pull electrons from a 'cold' source in good vacuum. A commonly used method is to use a very sharp tip like is used in a field emission source in a electron microscope.

http://en.wikipedia.org/wiki/Field_emission_gun
http://sites.bio.indiana.edu/~cryo/images/FEG_Tip_001.jpg

Matterwave
Gold Member
An electron microscope usually only has the electron jumping very very short distances though right? For a macroscopic separation of the capacitor plates, I would think a ridiculously strong electric field might be needed.

UltrafastPED
Gold Member
An electron microscope usually only has the electron jumping very very short distances though right? For a macroscopic separation of the capacitor plates, I would think a ridiculously strong electric field might be needed.

My photo-electron guns had about 5 mm from the cathode to the extraction grid (grounded); the design intent was to support 30,000 volts so that the electrons would have 30 keV as they pass through the extraction grid ~1/3 c.

Any sharp edges resulted in cold cathode emissions (as NSASPOOK mentioned); the vacuum was 10^-9 torr, just at the edge of the ultrahigh vacuum regime. If you do the calculation the field strength is 6 MV/m.

To get rid of sharp edges requires good design, good machining, and lots of polishing. A mirror finish is the desired final state.

For a transmission electron microscope the electron optics column is quite long; a couple of meters for typical modern systems. There are several designs for the emission tip; the older ones used thermal sources with sharp tips, the newer ones use cold emission techniques with atomically sharp tips.

The electron optics usually consists of magnetic lenses, with perhaps some electrostatic devices at the very beginning. Just a few electrons at a time, but at a steady and rapid rate provides a very narrow, intense beam of electrons at the target.

Electron microscope designs: https://en.wikipedia.org/wiki/Transmission_electron_microscopy

nsaspook