Electron path in the presence of a dielectric

[kelly0303]

Hello! Assume that I have a parallel plate capacitor. If i place an electron close to the negative plate, it will move in a straight line (and accelerate) towards the positive plate. Now, assume that I place a neutral dielectric close to the electron trajectory (parallel to it), say at 1 mm away from its trajectory (so the electron is still traveling in vacuum). Will the electron trajectory be affected by the dielectric, or it will still travel in a straight line? And in case it is affected, is there any material/configuration I can use instead of the dielectric to have as little deviation as possible (I need to place some device inside 2 parallel plates, such that the field inside is as little as possible affected by that device)? Thank you!

 

[phinds]

Hello! Assume that I have a parallel plate capacitor. If i place an electron close to the negative plate, it will move in a straight line (and accelerate) towards the positive plate.

It will travel ALONG THE WIRE. If the wire is straight then you can call it a straight line. I think you are very confused, however, because you are assuming it will reach the positive plate. It will not, unless (1) the plates are touching, in which case you don't actually have a capacitor, you just have a wire that widens out at one point, or (2) your voltage is great enough to overcome the dielectric strength of air, given the distance between the plates, then you have dielectric breakdown and a spark. Otherwise, it will just accumulate on the negative plate (assuming the cap isn't already full charged).

Now, assume that I place a neutral dielectric close to the electron trajectory (parallel to it), say at 1 mm away from its trajectory (so the electron is still traveling in vacuum). Will the electron trajectory be affected by the dielectric, or it will still travel in a straight line?

Same issue as above. The introduction of a "neutral dialetric" does nothing to stop the electron from accumulating on the negative plate.

And in case it is affected, is there any material/configuration I can use instead of the dielectric to have as little deviation as possible (I need to place some device inside 2 parallel plates, such that the field inside is as little as possible affected by that device)? Thank you!

Since you only get the electrons to travel between the plates by cause a spark, this is really irrelevant.

The beginning of your post appears to be about electron flow while the end of the post apprears to be about the field between the plates. It's a good idea to better separate your questions.

 

[kelly0303]

It will travel ALONG THE WIRE. If the wire is straight then you can call it a straight line. I think you are very confused, however, because you are assuming it will reach the positive plate. It will not, unless (1) the plates are touching, in which case you don't actually have a capacitor, you just have a wire that widens out at one point, or (2) your voltage is great enough to overcome the dielectric strength of air, given the distance between the plates, then you have dielectric breakdown and a spark. Otherwise, it will just accumulate on the negative plate (assuming the cap isn't already full charged).
Same issue as above. The introduction of a "neutral dialetric" does nothing to stop the electron from accumulating on the negative plate.
Since you only get the electrons to travel between the plates by cause a spark, this is really irrelevant.

The beginning of your post appears to be about electron flow while the end of the post apprears to be about the field between the plates. It's a good idea to better separate your questions.

Thank you for your reply. I am not sure what you mean by the wire. I am talking about the space in between the 2 plates. There, we have an electric field so if we place an electron at a point in between the 2 plates, it will accelerate towards the positive plate (this is the basic principle used in particle accelerators). You can just ignore the existence of the plates completely and imagine an electron in a constant electric field. I mentioned the plates to have a concrete example. So my question is, if I place a dielectric close to the electron trajectory (which is a staright line in an uniform electric field), will the trajectory change, or will it still be a straight line?

 

[phinds]

Thank you for your reply. I am not sure what you mean by the wire. I am talking about the space in between the 2 plates. There, we have an electric field so if we place an electron at a point in between the 2 plates

AH ... BETWEEN the plates. My whole comment was about an electron in one of the wires. Guess I really wasn't paying attention.

 

[gneill]

The field produced by the dielectric will be parallel to the field produced by the plates. It's a field induced by the plate field in the material comprising the dielectric. I don't think that it could effect the electron traveling outside the dielectric.

 

[kelly0303]

The field produced by the dielectric will be parallel to the field produced by the plates. It's a field induced by the plate field in the material comprising the dielectric. I don't think that it could effect the electron traveling outside the dielectric.

Thank you for this! I was mainly wondering if the field lines will still be parallel, or will they go inside and outside the dielectric (as it will have zero potential).

 

[sophiecentaur]

An improved model for the OP would probably be the electron traveling through a cylindrical hole inside the dielectric. In that case, the Field would be normal to the plates and ensure symmetry and the electron motion would be the same for identical Voltage and Separation (E = V/x). Introducing the dielectric when the supply was turned off would mean that the Q would be the same and Voltage would reduce (Q=CV) and so the Field and Acceleration would be less.
There are a host of alternatives to a question like this, depending on which variables are kept constant and which ones are changed.

 

[ZapperZ]

Hello! Assume that I have a parallel plate capacitor. If i place an electron close to the negative plate, it will move in a straight line (and accelerate) towards the positive plate. Now, assume that I place a neutral dielectric close to the electron trajectory (parallel to it), say at 1 mm away from its trajectory (so the electron is still traveling in vacuum). Will the electron trajectory be affected by the dielectric, or it will still travel in a straight line? And in case it is affected, is there any material/configuration I can use instead of the dielectric to have as little deviation as possible (I need to place some device inside 2 parallel plates, such that the field inside is as little as possible affected by that device)? Thank you!

Actually, the presence of the dielectric CAN produce a change in the field inside the capacitor. It depends on permitivitty of the dielectric. The electric field near the dielectric will bend.

We had a HW post a while back asking about something similar with a spherical dielectric:

https://www.physicsforums.com/threads/insulator-in-an-electric-field.843772/

Zz.

 

[gneill]

Actually, the presence of the dielectric CAN produce a change in the field inside the capacitor. It depends on permitivitty of the dielectric. The electric field near the dielectric will bend.

We had a HW post a while back asking about something similar with a spherical dielectric:

https://www.physicsforums.com/threads/insulator-in-an-electric-field.843772/

Zz.

Pretty sure that a rectangular slab of dielectric extending from plate-to-plate will not effect the field outside of it. All the field lines encountering the slab will be normal to it, and remain parallel. There won't be any surface charge expressed by dielectric activity along the path of the electron.

 

[ZapperZ]

Pretty sure that a rectangular slab of dielectric extending from plate-to-plate will not effect the field outside of it. All the field lines encountering the slab will be normal to it, and remain parallel. There won't be any surface charge expressed by dielectric activity along the path of the electron.

I don't see why the field lines can't bend. For example, if I half-filled the capacitor with a dielectric, so that there are field lines going from + to - electrodes of the capacitor just above the surface of the capacitor, wouldn't the induced polarization causes those field lines to bend and enter the dielectric, and thus, disrupting the field lines near it?

The electric field lines need not be normal to the surface for a dielectric, unlike a metal.

Zz.

 

[gneill]

In the case of the spherical dielectric there are surface charges presented along the curved surface which can interact with the external field. In the figure from the quoted post:

note that the field line entering the "equator" of the sphere is undeflected.

For the plate capacitor all of the induced fields are parallel to the main field, and no surface charges appear along the sides of the dielectric (I've ignored fringe effects at the edges of the plates):

 

[hutchphd]

But the fringe effects are likely the crux of the issue!
Can @kelly0303 please describe her proposed geometry and size specifications. In general there will be a nontrivial effect from the polarization charge.

 

[ZapperZ]

In the case of the spherical dielectric there are surface charges presented along the curved surface which can interact with the external field. In the figure from the quoted post:

View attachment 256095

note that the field line entering the "equator" of the sphere is undeflected.

For the plate capacitor all of the induced fields are parallel to the main field, and no surface charges appear along the sides of the dielectric (I've ignored fringe effects at the edges of the plates):

View attachment 256096

But the fringe effects are likely the crux of the issue!
Can @kelly0303 please describe her proposed geometry and size specifications. In general there will be a nontrivial effect from the polarization charge.

Yeah, I think that's where we differ because I do consider the sides and corners of the dielectric.

But there is another aspect here that hasn't been considered, and it isn't negligible, even though it may not be within the scope that the OP is thinking of: image charge. Even if the electron's path is parallel to the surface of the dielectric, there will always be an image charge in the dielectric, which will mess with the electron's trajectory.

This, and the creation of wakefield in the dielectric structure, are two phenomena that those of us working in dielectric-loaded accelerating structures in particle accelerators often have to deal with.

Zz.

 

[sophiecentaur]

The electric field near the dielectric will bend.

But the fringe effects are likely the crux of the issue!

There are many links to this effect.
This one seems pretty rigorous and the diagram shows how the field near the edge is not normal to the plates. This will be present with or without a dielectric. Hence my suggestion that considering a hole through the dielectric would not involve an edge effect.

 

[gneill]

I like @sophiecentaur 's suggesting of using a drilled hole. It should also mitigate the image charge issue as there will be equal images in the surrounding wall. Just be sure to center the electron's path in the hole.

I found an on-line java applet here that allows you to set up a configuration of charges, charged plates, charged conducting plates, dielectrics, and a host of other options. The resulting electric field lines are calculated and displayed to varying accuracy.

Here's an screen snip of what I set up:

The blue blocks are charged conducting planes. Positive on top, negative on the bottom. The brown blocks are dielectric material.

Here's the resulting electric field:

The simulator interface is a bit glitchy, like losing the distinctive material type colors at random (that's why you can't distinguish the dielectric from the plates in the above image). It is interesting to add dielectric bits one at a time and watch how the electric field alters.

 

[gneill]

Interestingly, the presence of a dielectric seems to mitigate the some of the edge effects (fringing) at the edges of the plates. Here's a run with the capacitor half-filled with dielectric material:

This time the interface didn't lose the material coloring.