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zarbanx
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i wanted to ask why the electric field inside a hollow conductor zero throughout and not just at the centre.
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zarbanx said:okk as u say well i have done a lot of work and research i know tht there is no electric field inside a conductor bt i am not able to prove it mathematically and moreover electrical charges in conductors move to the surface becoz no electric field is there in a conductor becoz if there is a field then charges will move to neutralizze it.when an external electrical field is present then charges rearrange tso that no electric field is there in the conductor bt still mathematically i am not able to prove it
berkeman said:(which text are you using?)
zarbanx said:i am using resnick and halliday
Isaac Newton used what is called "Shell Theorem" to rigorously prove some important things about spherical shells, one of which is what I mention above, and another of which is that any spherical object can be modeled as a point mass when you are located outside the object.
zarbanx said:that means in an external field there can be a net field inside the hollow conducting shell
merryjman said:I'm not sure that's true. What happens in an external field is that the conductor will become polarized, and it polarizes in such a way that the field inside is still zero.
Ulysees said:Merryjman, are you familiar with the math involved in here? I have got stuck in another similar problem:
https://www.physicsforums.com/showthread.php?t=212711
merryjman said:If the electric field inside a conductor was NOT zero, then there would be a force acting on the mobile charges, and so they would rearrange until the force WAS zero.
merryjman said:But if the force was non-zero inside, charges would still be moving
Inside a conductor, charges are free to move. If there were a non-zero field there, they'd move. (They move until the field is canceled.)Ulysees said:Why? The field inside need not be identical to the field on the surface. Might be zero inside and non-zero on the surface or vice versa when equilibrium is reached.
Doc Al said:Inside a conductor, charges are free to move. If there were a non-zero field there, they'd move. (They move until the field is canceled.)
Why do you say that there are no charges inside a conductor? There is no field inside a conductor.Ulysees said:In equilibrium there are no charges inside. So electric field inside can be non-zero in equilibrium (under the influence of an external field always).
Wrong again. On what basis do you say this? The field inside a conductor does not depend on the shape of the conductor.Even without an external field, if the object is not spherical the electric field inside will be non-zero, in equilibrium. That's for a charged object of course.
Ulysees said:In fact an electron on the surface might experience no net force (in equilibrium) but still produce a field of its own in its vicinity. So equilbrium of electrons does NOT imply zero electric field around them.
In fact an electron on the surface might experience no net force (in equilibrium) but still produce a field of its own in its vicinity. So equilbrium of electrons does NOT imply zero electric field around them.
merryjman said:True, but it does imply zero NET field, in terms of vectors.
I admit (and apologize) for being a bit patronizing. But it's you who are saying incorrect things. OK, you mean no NET charge within the conductor. I'll give you that one.Ulysees said:Doc Al I am sorry, but you are saying incorrect things and in a patronizing way. It is well known that charges accumulate on the surface of a conductor when equilibrium is reached. Shall I dig up the relation between curvature and charge density, or you agree now?
In electrostatic equilibrium, the field within a conductor is zero. Regardless of shape. Don't think so? Tell us why.So in equilibrium there is no charge inside. And electric field can be non-zero, which it will be if the object is a cube say.
I'm not understanding the relevance of this to the fact that the field within a conductor is zero. (Of course if you start sticking charges inside it you've destroyed equilibrium.)If you put a charge inside any object, you'll have to hold it there, otherwise the charge will go to the surface. It will move under the influence of the non-zero field caused by the other charges redistributing on the surface.
Except if the object is a sphere and you hold it at the centre, no re-distribution of surface occurs then and the charge you put stays at the centre of the sphere itself.
What does this have to do with the field inside a conductor? In a conductor, you can redistribute as many electrons as needed to cancel any external field. (Of course, if the external field is so incredibly humongous that all available electrons within the conductor are still not enough to cancel the field--then all bets are off. )Ulysees said:Imagine just 4 electrons in a circular disk. They'll form a square. Each will be in equilibrium. But in the vicinity of each electron the e-field will be non-zero. Shall I draw a diagram and calculate the e-field somewhere in the middle between electrons, on the surface?
Are (the 4 electrons) attached to the disk? Or are you picking 4 electrons on the edge of the disk? Why?
Ulysees said:The field inside can be calculated numerically for any conductor based on the relation between surface curvature and charge density. For most charged conductors, the sum will NOT be zero. Take a cube for example. All charge goes to the corners of the cube. This is predicted by the relation between curvature and charge density. Shall I draw a cube and the related 6 E-field components?