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Conceptual issues with "electric field inside a rotating cylindrical conductor" problem

The problem posed last week confused me quite a lot. Frankly speaking, I could not understand physics of that problem and when finally I saw the solution, I am confused even more. This is because most of the solutions given simply balance magnetic force value to centripetal force value. But I don't think that physics of the problem is clear from this. In particular, I have following questions:

(1)Will "all" the free electrons inside the cylinder move to surface ultimately? If not, what is stopping them?

(2)As many given solutions say, there has to be electric field inside to provide necessary centripetal force. But then how is that field generated? I mean, how a motion of a particular electron causes some field to be created?

(3)Why the motion of charged particle in electric and magnetic fields will be such that internal fields are exactly canceled?

I hope that people would respond. Thank you :)

Note by Snehal Shekatkar
3 years, 11 months ago

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For reference, here's a link to that problem so that people can discuss it.

David Mattingly Staff - 3 years, 11 months ago

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Thanks for the link.. :)

Snehal Shekatkar - 3 years, 11 months ago

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Hi David, i just solved the question but i can't access the discussions.

Jatin Yadav - 3 years, 11 months ago

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In case of a pure conductor we consider all conductors are free and can move, so when cylinder rotates a force acts on it which pushes it outwards , so charges will exist in periphery, in absence of magnetic field ,force due to electric field is equal to centripetal force , now we consider d case with magnetic field , as we dont want electric field , we want to equate centripetal force with force due to magnetic field , to prevent outward movement of electron , it also should be stated if magnetic field exceeds centripetal force movement of electrons would be inwards

Avinash Iyer - 3 years, 11 months ago

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I think it is better to resolve issue of creation of electric field before we talk about suppressing it using magnetic field. For sure, if at all, free electrons are thrown out to surface, that is just because they acquire speed because of initial impulse, after that no force is acting on them till they reach to the surface. I think people would not disagree with this. Now, suppose our conductor is not ideal so that there is no infinite supply of electrons, still for me it is surprising if ALL the electrons go the surface (which would mean that volume charge density is zero!). Now, suppose that this actually happens (does this effect have any name in the theory of electromagnetism?). But then if we switch on the magnetic field, electrons will be pushed in again. But wait a minute! Now these electrons have nonzero speeds and hence magnetic force would keep acting on them and the distribution inside the conductor should keep changing! How on earth then the electric field ever be zero?? Lets discuss and sort out this issue. Hopefully, after enough discussion if we don't resolve the issue, David sir will guide us. :) Thank you

Snehal Shekatkar - 3 years, 11 months ago

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If no electric field is created, can we allow for any redistribution of charge in the conductor when it starts rotating?

David Mattingly Staff - 3 years, 11 months ago

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@David Mattingly Of course not. Certainly redistribution of charges would create electric field. The only issue is to understand why at all electrons will redistribute when cylinder starts rotating and exactly what will be the distribution.

Snehal Shekatkar - 3 years, 11 months ago

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A continous centripetal force continues to act on the electron as it is moving outward and as it moves outward regional charges appear causing an electric force as well but this dynamics is quite hard to deal with , and ur 2nd statement , the fact is all electrons dont go , to the periphery,(not even in case of pure conductor) a particular amount of charge is delocalised , which makes it clear that only some electrons go to the periphery , and centripetal force always acts on the electron its just balanced by the electric field , as magnetic field is turned on , electron start returning to their original state , again dynamics to tough to deal with

Avinash Iyer - 3 years, 11 months ago

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@Avinash Iyer I don't think that centripetal force keeps acting on them. This is because they don't move in circular orbit around the axis. Rather they go tangentially in a straight line!

Snehal Shekatkar - 3 years, 11 months ago

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@Snehal Shekatkar Thats ur mistake , they have to move continously , ur assertion means that electrons are floating in air , that is not possible

Avinash Iyer - 3 years, 11 months ago

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@Avinash Iyer That is what is meant by free electrons. Did you study solid state physics so far?

Snehal Shekatkar - 3 years, 11 months ago

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@Snehal Shekatkar Well i havent studied solid state physics , well in that case if what ur saying is true then i dont think i am capable of making any further reasoning

Avinash Iyer - 3 years, 11 months ago

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@Avinash Iyer Free electrons are completely free inside the conductor. If you give even a small impulse to any of them, it will move in a straight line till it reaches the surface. At the surface it experiences practically infinite potential so it cannot leave the surface.

Snehal Shekatkar - 3 years, 11 months ago

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I don't understand why people who voted up this discussion before, again voted down. :(

Snehal Shekatkar - 3 years, 11 months ago

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i sorta see what you mean, i wrote one of the solutions for it but have had doubts about my reasoning ever since.. mainly because if the centripetal force is being countered by the magnetic force completely (so that no electric field is generated) then i don't see how everything doesn't just fly off out of the cylinder because there is no net inward acceleration if the net force is 0 ofc.... among other confusing parts of the question too... i blame my lack of experience in electromagnetism lol

Jord W - 3 years, 11 months ago

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Lets talk about situation without the magnetic field. In the first place, why should electric field be generated? So initially, let us say free electrons are at rest w.r.t. conductor. Now we give impulse to cylinder and it starts rotating. My first thought was that then free electrons as well receive impulse and will start following tangential paths and will accumulate on the surface. But then all the free electrons should do that. And the whole inside of the conductor should contain no free electrons! If this really happens, then its too amazing and I thought that this effect would have some name. But I don't see any such effect described in well known books like Griffiths and Feynman lectures. I am still confused by the way.

Snehal Shekatkar - 3 years, 11 months ago

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