Usually we say that the charges will redistribute over the surface of the sphere so that the net electric field inside a conductor becomes zero. But in the above case, there exists no possible charge distribution (of course, keeping the quantisation of charge in consideration). Quantum theory seemingly suggests that by superposition, the electron can be at two different places at same time. But, at such macroscopic level, is it possible for superposition to play effectively?
Dear Gaurav ,
If I understood your statement correctly, then you find it hard to conceive how one electron can distribute itself to produce a uniform charge density. My answer would be, in the same way as 1000 electron will do so!! I think when a lot of electrons are involved, you would like to think of it as if 500 electrons in the left half and 500 electrons in the right half. But in principle you can divide the sphere into smaller and smaller portions and eventually you will reach at a sufficiently small piece containing no electron. So, what is meant by uniform charge density?
As I feel, the problem lies in thinking that the electrons are 'glued' on the body of the sphere in the perfect positions. Talking in terms of classical physics, the electrons are constantly moving on the conducting body and when we talk about macroscopic quantities, what we really mean is their "time averaged value". This 'time period' is really very small in a macroscopic sense. (Remember Perrin's work in brownian motion). So, when this 'one electron' moves on the sphere it CAN PRODUCE "fractional charge per unit area" constant throughout the sphere without bothering about the requirement of fractionally charged particles.
Regards,
Dipankar
A conductor is not the same as free space. Within any conducting sphere that can be reasonably termed "macroscopic" the probability distribution for conductance-band electrons is distributed over the entire volume. So yes, the charge may as well be distributed over the body's surface for all practical purposes of field measurement, even though the net charge of the sphere is quantized. Keep in mind that adding an electron to the macroscopic sphere alters the effective charge distribution of all the other electrons; there is no meaningful way to measure the electric field of the one electron in isolation.
In this case , the electron will wonder freely in the sphere, if the sphere is a monocrystal. The thermal velocity of the electron is very high some tens of thousand m/s , but it will continuously collide with conductor ions..
"School" theory of electricity can be useful for solving "school" tasks. This theory does not into account many "physical" features. Quantization of charge is only one of them.
Question has no sense in frame of more detailed physical theories of electricity
If the spere is real and placed in atmosphere; there won't be any free charge on it's surface. If the spere is real but in vacum, now how can it's surface's charge be measured. And how this surface charge has been induced and kept constant in the first place. One way for reaching it's equilibrium state would probably consist in changing (almost unobservabely) it's internal structure - for sure a real spere would has a lot of lattice defaults (not to mention that it is probably policristaline with more than one lattice and some amorph inclussions) - which by modifying woud provide the equilibrium state. You could have limited to a spheric shape made of a few atoms - then the lattice perfection would have become more probable and the electron's movement with a very fast speed on the surface of the spere would have become more obvious. Even the lattice modification in order to fix the electron on some atom's energy level would be more easy to understand. But this last object would not be so real. It's very intresting how "nature" provides itself with a lot of anomalies in order to ensure a greater diversity of possibile solutions. This is why there have been formulated a lot of probabilistic theories to cope with such diversity.
By Gauss' law the electric field of a charged sphere is the same as a point charge at the center (this is a mathematical equality). The field is zero inside a conducting sphere, though.
None are right! The answer is that the charge will exist on the outer surface of the sphere and Maxwell's displacement current will exist within the sphere.
Ist of all, suppose we put 'q' amount of charge at one place on a conducting sphere then the charge will get uniformly distributed over the sphere (obviously by disturbing other electrons in the conductor). And the charge density will be q divided by the surface area of the sphere. This charge density at a point doesn't mean that integar multiple of electronic charge will be present at a particular point on a sphere. In the same sense if we place 'e' amount of charge on a sphere, then it will disturb the other electrons in a way that there will a total charge equals to 'e' will get uniformly distributed over the sphere. So the field inside the conductor will be zero.
A concept of elementary electric charge was introduced in physics in 1874 by J.Stoney. It appeared useful for many macroscopic electrodynamical phenomena. But when we have deal with an electron Maxwellian electrodynamics becomes incorrect. Electric charge is manifestation of electron spin, whose negative polarization (i.e. when spin is antiparallel to the velocity) corresponds to electron, while positive polarisation (spin is parallel to the velocity of particle) corresponds to positron. Therefore, position of any electron can be considered as a point on the nonconducting sphere. Field of the electron in any point will be depended from spin direction, distance and velocity of the electron relative to this point. This law is now unknown, but it is not Coulomb law.
Dear Gaurav ,
If I understood your statement correctly, then you find it hard to conceive how one electron can distribute itself to produce a uniform charge density. My answer would be, in the same way as 1000 electron will do so!! I think when a lot of electrons are involved, you would like to think of it as if 500 electrons in the left half and 500 electrons in the right half. But in principle you can divide the sphere into smaller and smaller portions and eventually you will reach at a sufficiently small piece containing no electron. So, what is meant by uniform charge density?
As I feel, the problem lies in thinking that the electrons are 'glued' on the body of the sphere in the perfect positions. Talking in terms of classical physics, the electrons are constantly moving on the conducting body and when we talk about macroscopic quantities, what we really mean is their "time averaged value". This 'time period' is really very small in a macroscopic sense. (Remember Perrin's work in brownian motion). So, when this 'one electron' moves on the sphere it CAN PRODUCE "fractional charge per unit area" constant throughout the sphere without bothering about the requirement of fractionally charged particles.
Regards,
Dipankar
firstly, thank you all for such a nice response and I wish to clarify that I just assume that such a sphere, whatever its size may be is given to me with a net quantum of charge. I would like to point one thing out here. As many of you suggested that the electron would be moving all over the surface of the sphere, hence producing fractional charge distribution in a way. In that case, what I think is that the electron would continuously lose energy and the charge may itself get trapped by nucleus of some atom. Does this make some sense or would it take a long time?
And dear Wave Rogue, sir, I posted the question as it came into my mind while discussing the topic with a friend. So i just thought ResearchGate as good option to put it up.
Thanks to all once again.
Ok... I am sorry and thanks Mr. Xavier. I just concluded the last point too quickly, also, of course I am still pursuing my graduation, so I am not that much familiar with the ''Quantum Concepts". Thanks to all for giving your time to answering my query. Still could you people suggest me how to approach such cases?
Alright, about the charge... exactly! Well, Maxwell's equations are time average phenomena and quantum mechanics crawls under the hood. The charge can be spatially or temporally local at any given point in time anywhere on the surface of the sphere... So, it does not have to be "equally distributed". It is possible for the electron to go deep into the sphere, but this is unlikely, because of the collisions encountered with the lattice.
Oh, by the way; a very good question Gaurav, indeed. Maxwell's equations are based upon experiment, thus, the aggregate behavior. Quantum mechanics is pure metaphysics, based upon a transport equation alone! It is good to ask such metaphysical questions, even though there might not be a clear answer! What it does do is force you to really think about the physics, as we understand it... or maybe, as we don't understand it! My answer is simply as I understand it...
And one more thing... I was involved in an experiment to test a DC discharge for disabling automobiles for human safety effects. We did a lot of work and found out, much to our surprise, that no one knows exactly how many Coulombs of charge exist on the sphere before it discharges. I know what everyone will say, "use the formulas and calculate the charge density." The fact is that we measure observables like current, magnetic field strength, &c. But to measure or collect in a jar x amount of electrons, well, my friend, that is quite a challenge. Also, it is an academic exercise. Practically speaking, you would never be able to measure one electron nor notice what that single electron does in the macroscopic realm. Also, even an electron gun emits electrons in some distribution, but we never speak of that distribution, we speak of the time average; because, that's all we can observe and measure. No one speaks of a single electron from an electron gun and that they were ever able to measure it!
One more thing, Gaurav, I mentioned Maxwell's displacement current... you need to think about that one more. It's quite remarkable what is states, but even in a vacuum, there is a current! This current could be said to emanate from the Dirac Sea, but that's metaphysics at it's best! So, no matter what charge is placed upon the surface of the sphere, the charge will reside primarily upon the surface of that sphere, also, there will exist a minimum current within the sphere, that current is Maxwell's displacement current. When Maxwell was forming the first "Theory of Everything", he combined all the existing electromagnetic equations, all these were derived from experiment; but, to maintain symmetry, he found it necessary to add the "Displacement current". So, is theory right? Is there a displacement current? Is it that it exists in the equations for purely aesthetic reasons? They have in fact measured the displacement current, experimentally, the so-called Casimir effect!
see link: http://www.casimir-network.net/IMG/pdf/Casimir_20effect.pdf
A word about quantum mechanics... it is purely based upon an idea, that of a transformed transport equation. Yes, it has been verified by experiment, in fact, it is referred to as "the most successful theory" of all time! Nevertheless, it is pure metaphysics. Electromagnetic theory began with experiment and ended with a theoretical summit in Maxwell and Einstein. I only bring up the issue of metaphysics, because it was used to trump arguments earlier in the chain of comments within this blog; for me, it is quite impossible to get away from metaphysics!
Here, here... So true Wave Rogue... They call it the disappearance of substance philosophy, i.e. the belief that matter is made up of 'stuff', stuff that may be considered concrete and real and every attempt to identify that stuff leads to yet smaller and smaller, even exotic 'stuff'! All of it has degraded into shear nonsense! The only saving grace of it all is the inherent "power of manipulation" that any one theory may engender. Least we forget we are only monkeys, hence, the power of any scientific theory is the ability of that theory to enable us some modicum of power over matter, i.e. to make a device that does something. Many have spoken of the "end of science", since the 90's, which I might add I believe is quite true. We have less and less available to us to 'investigate'; moreover, the energy required for the 'next discovery' is far surpassing our wildest dreams! Even the discoveries of today, particle physics, have very little pragmatic virtue associated with them; hence, really, what is the purpose of it all! Thus, its all metaphysics... even a religion, to some degree?
Thank you Luisiana, Wave Rouge, etal. Marvelous to watch intelligent people discuss important subjects. Luisiana, dont worry, ideas will triumph over energy!
Well, calling QM "pure metaphysics" does not belong to an intelligent discussion :).
@Wave. There's very little "incomprehensible" about QM. It's a fully consistent theoretical framework, with clear and testable (and tested!) predictions (where it applies). The fact that we cannot relate our everyday experiences to QM is because of our own limited senses. There are many phenomena in classical physics as well, which go against our "instincts", but this does make classical physics "incomprehensible", either.
@Luisiana. Your outline of the philosophy of science is certainly the most original one I've ever heard :). I've read my Wittgenstein and Nietzsche, and they're not to be invoked when discussing philosophy of science :).
@Nilotpal. There's a space science topic as well as a climate change topic, where you can post your argument(s). However, I should warn you that what you state in your post makes no sense as it is. EM radiation is exactly what warms up Earth, not particle (solar) wind, so of course it controls the climate! If you wish to elaborate, please start a new thread on the other topics. Off-topic posts should be cleaned away from this topic. Br, Tapio.
The sphere is conducting, therefore when the 1 electron comes from infinite and attaches to the sphere, the rest of the electrons in the sphere will re-arrange, their current position will be perturbed away from the new electron, to uniformly distribute the 'charge' across the sphere's surface area. So, there is a charge distribution that is possible.
This sentence is only true for a non-conducting surface: No electron will be removed from it's atom, as the outermost shell electron clouds will be 'bent' out of shape.
For a conducting sphere, there are free electrons in the conduction band, and these free electrons will re-arrange into an uniform surface charge.
QED at work.
At the macroscopic level, all 'effects' are a summation of the microscopic superposition effects. That's physics (QM) at work.
Conducting sphere is nothing else but constraints within which an electric charge may move freely. If there is only a single charge, then it may rest in a some point or move with constant velocity along a big circle, with no dissipation - if we neglect the radiation losses. This second scenario is by no means static and corresponds to a current loop generating magnetic field, and, consequently, permanent magnetic moment of the entire system. Very funny, indeed. After we add thermal fluctuations, forcing the charge to change its movement randomly, all we get should be noise. Both inside and outside the sphere. How do you like it?
An interesting answer, but what's the status of Gauss's Law in your view? Can the noise inside, by any possibility add up to zero?
There is no explicit time in Gauss Law, therefore it applies only to strictly (electro)static situation. Even if the time-averaged electric field vector was zero (it should, for symmetry reasons) then the same need not to apply to noise power, being proportional to .
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