Exploring Electric Fields in Conductors: Spheres, Cages, and Beyond

[Crazymechanic]

Ok again I'm thinking some things but a simple question,

You have two metal spheres , one inside the other.Now we know long ago from Faraday that closed metal spheres or cages or etc that are at some potential above ground tend to have their charge at the outside of the conductor in this case the sphere.

Now the inner sphere is a some - potential and the outer one at some + potential between those two is a vacuum, for theoretical reasons let's say a perfect vacuum.
Now we build up the potentials , how do the electric corresponding electrical fields of the spheres interact ? The outer + sphere has it's field on the outside but the inner one has it's field on the outside two which happens to be the inside of the larger + sphere , now because there is vacuum is there a chance of electric breakdown between those two spheres like a "short circuit"?
Also what would the inner - spheres field do to the outer sphere? How would it influence it ?


also can someone give me a good material or link to read about electric fields on various shapes of conductors , spheres , cages etc? In other words how do the fields enclose or what lines they have in different bodies.
Thanks.

 

[Drakkith]

I don't know the answer to most of your questions, but I can say that there would be a chance for dielectric breakdown if the potential difference between the two sphere is high enough. Of course, since the dielectric is a vacuum, I'm not quite sure how that would work in the case of a "breakdown".

 

[sophiecentaur]

It will depend upon just how good a vacuum you've got, the temperature and the work function of the metals involved how many electrons will be released from the negative surface. Once an electron has become free, it will travel across but, with no atoms to collide with, there will be no avalanche effect. (Unless it causes ionisation at the positive surface, perhaps)

BTW, the field exists between the spheres and does not 'belong' to either one in particular. The field (volts per metre) will be more or less the difference in potential divided by the separation (but modified slightly by the spherical geometry). Slightly higher near the inner sphere than the outer one - so the situation would not be quite symmetrical if the polarities were reversed as the current would be carried by electrons.

 

[Crazymechanic]

Well you say that " the field exists between the spheres" , but for the larger sphere (number 2) being positive the field exists only outside the sphere because as in a closed circle like a sphere the charge resides on the outside of the sphere hence the field pointing outwards , so does that mean that in the picture I draw the + field is only outside and doesn't affect the - or negative field of the first sphere?
Now the first sphere is negative and again a sphere so the negative field should be pointing outside it towards the inner side of the second sphere , but if these two metal spheres especially the first one are being kept at low temperatures like a maximum of 100 celsius then i guess no electrons should escape from the primary smaller sphere to make a path towards the secondaries inner side to start conduction?

And if the vacuum is good enough there should be no electrical breakdown too right?
If I remember correctly electricity can flow through vacuum only if there is a path of particles to form it's flow like a thermionic emission of electrons from a cathode in a vacuum tube ?

 

[sophiecentaur]

Well you say that " the field exists between the spheres" , but for the larger sphere (number 2) being positive the field exists only outside the sphere because as in a closed circle like a sphere the charge resides on the outside of the sphere hence the field pointing outwards , so does that mean that in the picture I draw the + field is only outside and doesn't affect the - or negative field of the first sphere?
Now the first sphere is negative and again a sphere so the negative field should be pointing outside it towards the inner side of the second sphere , but if these two metal spheres especially the first one are being kept at low temperatures like a maximum of 100 celsius then i guess no electrons should escape from the primary smaller sphere to make a path towards the secondaries inner side to start conduction?

And if the vacuum is good enough there should be no electrical breakdown too right?
If I remember correctly electricity can flow through vacuum only if there is a path of particles to form it's flow like a thermionic emission of electrons from a cathode in a vacuum tube ?

You need to get back to some basics here:
This is a misconception, and an extrapolation on what you know (correctly) of a simpler system. Potential is what counts (Energy energy energy is always the thing to start with! The field inside a charged shell is zero, only because of the mutual effect of the charges, distributed around the shell. When you have another sphere inside, there are a whole lot more charges and it will require Energy to go from one sphere to the other (involving positive or negative energy depending on the direction and on the different polarities for the shells). Perhaps it would help to remember that the Potential inside a charged shell is not zero - it is just 'evenly spread' throughout the empty sphere, which is why the Field (Gradient of the potential) is zero.
No!. A field is not 'negative or positive. It is a vector with a direction. You must look at a textbook, Wiki or Hyperphysics to get this stuff straight in your head if you want to get anywhere.

This is more correct. If there are no charges to move through a (good enough) vacuum then there will be no current. Any gas molecules in the space can become ionised, with a high enough field. If the field at a surface is high enough and in the right direction, it can also pull electrons off the (-) surface. The inner sphere has smaller radius so the field will be greater (See Wiki images of fields around curved surfaces) so + outside and - inside sphere can cause a flow of electrons. If these electrons have enough energy by the time they reach the outer sphere (PD between the spheres minus the work function energy needed to strip the electrons) they can disrupt the surface and knock metal ions off, which will travel in the opposite direction and you can expect a runaway situation as the current increases and increases. A power supply would be needed for this to continue, of course.

 

[Crazymechanic]

Yes I know the E field can't be positive or negative , I actually wrote that in the other question , I just messed up this question a little.

Ok so here goes for the final idea I had in mind.
What happens if I make the outer shell with evenly spaced small nanosized holes , holes that are just a little smaller than a ion ? Now normally if I would have ions at the outer + shell they would repel from the shell but if I have these holes and a negatively charged shell inside the outer shell how does the field from the inner sphere interact with the ions outside the bigger shell ?

Now I have a feeling that it would be hard for the inner sphere to attract those ions from the outer shell through the small holes as the electric field tends to cover small empty areas if there are charges around them just like a blanket can cover a hole if it is around it, but still I would like to know.

 

[sophiecentaur]

I can't visualise your thought experiment by I would say the way to resolve what would happen is to draw the setup and mark + and - potentials in the appropriate places. The negatively charged inner shell will produce a charge displacement (polarisation) on the outer shell (+ on the inside and - on the outside) in just the same way as any conductor becomes polarised in a field. Look up Electrostatic Induction, The Electrophorus and the Wimshurst Machine.

 

[Crazymechanic]

Now Sophie for you to be able to understand what I thought i made a drawing again , now I have two situations , both situations or models are the same (two shells or spheres one smaller and inside the other one being bigger.
The smaller one in both cases is at a given (-) potential , now in the first picture or model I made it as you mentioned about the polarisation , as the inner shell being at a minus potential the inner side of the outer shell gets positive as the minus charge from the inner one drwas the positive charge at the inner side of the bigger sphere , thus leaving a net negative charge on the outside of the bigger shell.
Now in the second model the inner shell again is at a given negative potential but the outer one is connected to a given positive potential for the sake of an argument let's assume a high voltage battery which has it's negative connected to the inner sphere and positive to the outer , and a vacuum between the shells to eliminate dielectric breakdown and a short circuit.
Now the first question is especially about this second case , what happens to the fields , or spheres and their charge as the inner one doesn't feel the positive charge because he field of the bigger one "gathers" so to say around the outside of it but the second larger one "feels" the first one.?

Also in both models there is a cone at the side of the outer sphere , think of it as a 3d cone built inside the outer sphere from the same material, it has an open end towards the inner sphere but the end is smaller than the size of a proton.Now we put some ions in that cone. The question is what do they feel ? Do they experience only repulsion due to the outer shell being positive or do they feel the inner negative charge at the small end of the cone and tend to travel towards it despite the repulsion getting bigger at the end of the cone because the cone get's smaller and the positive charges are more closely together hence the field stronger at that place?
I know it's a long question but I would be pleased if you or someone could take their time to think about it.

 

[Crazymechanic]

ups i forgot to attach the drawing so here it is. :)

 

[sophiecentaur]

If you add some + ions to the outer shell then you change its potential. The PD between shells is changed. The outer shell is still polarised. Why do you think anything is different about the situation? Anything that applies to electrons (nicely mobile) will also apply to other less mobile charges. The direction of any force will depend on the sign of the charge. That's all. Forcing charges in the way they wouldn't naturally go would need a local power supply which would alter potentials everywhere. Shell Theorem still looms in your mind, I think.

 

[Crazymechanic]

Ok I'll try to make this simpler , otherwise people sometimes don't get me.
Let's say i would like to confine protons or ions in those cones that are into the outer sphere.But because the sphere is at a high + potential the ions would normally be repelled , now I could put some plates that are separated from each other to have the field on both sides and that would confine the ions to the cones and the outer shell in general but now let's say i would like them to be drawn towards the inner smaller sphere which is at a - potential , those ions would normally want to go to that ground or negative potential but they can't because they have a sphere of positive charge in their way that repels them.but in the ends of these cones are left open and the thing that interests me is how the negative charge attracts those ions through those small tips left open in those cones.
you could almoust call this an electrostatic confinement , where with an electric field ions are being confined but to accelerate them and compress them you use a opposite polarity (the inner sphere ) and the cone because of the cone getting smaller at the tip the field is so much greater thus exerting a greater pressure on the ions which would push them back , the thing that I keep wondering is can a opposite polarity charge be felt through the small tip at the end of the cone to force those ions overcome the strong +field and let them escape through the tip thus accelerating them?

Now I understand that normally you could just direct me to a page where electrical field theories and math is written but I learn a lot from such models.

 

[sophiecentaur]

Do you not realize that forcing ions to go to somewhere involves Work. Hence, a change of potential. If your little cone is to work, it will need to be insulated. You then, no longer have a simple spherical symmetry. Work done will affect the system as usual.