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Electrical Field Inside a Charged Metallic Conductor

  1. Sep 22, 2003 #1
    Please read this topic first.
    I have recently seen a proof (using Gauss' law) showing that there is no electrical field inside a charged metallic conductor (due to the carge on its surface). (i can provide this proof if needed)
    If that proof was right, then this must mean that the inner sphere in the original question (see the link at the begining of the post) will not be charged.
    So, will or won't be the inner sphere get charged ?
    Thanks in advance.
     
  2. jcsd
  3. Sep 27, 2003 #2
    So ... no takers ?
    *Bump*
     
  4. Sep 27, 2003 #3

    drag

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    Greetings STAii !
    Hmm... I'm not quite certain what you're talking
    about, here's Gauss's Law :
    http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html#c1

    The POTENTIAL INSIDE (the inner sphere in this case) should
    be zero - which is going to be the case in the inner (conducting)sphere. Also, because it's conducting (in your previous example)
    the permativity is not going to be high. Further more, practicly
    there is no such thing as an infinite permativity since the
    atoms or molecules of every material have some level of
    potential electrical energy which they can not surpass and
    once it is reached the electrons will be separated from
    the ions as a discharge current.

    Live long and prosper.
     
  5. Sep 27, 2003 #4
    Here is a the proof (i hope my translation is ok).
    Now back to the original question.
    If this proof is right, then the electrons in the inner metallic sphere (in the original question) will not be affected by an electric force from the outer sphere, so the inner sphere will not have a negatively charged surface. Right ? (the question now is no more about the permitivity of the metal).

    Thanks a lot.
    (edited for formatting mistake)
     
    Last edited: Sep 27, 2003
  6. Sep 27, 2003 #5

    drag

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    But, when the outer shell is separated by a gap from the
    inner sphere you have a non-unform permitivity within.
    Further more, in a conductor the potential is 0 throughout
    the volume of the sphere when the charge is ditributed on
    the surface, but here, due to non-uniform permitivity
    and as long as the charge on the shell is not high
    enough to cause a discharge from the sphere, the potential
    inside is not zero.

    Live long and prosper.
     
  7. Sep 27, 2003 #6

    krab

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    Whoa. I looked at the original thread you referred to and it's WRONG. I don't know who the mentor was when the original thread appeared, but he must have been asleep at the switch. A spherical metallic shell completely shields its contents from electrical fields. You can charge it as much as you like; there will be no effect on the contents. In fact, the shell needs not be spherical. This is called a Faraday cage. Look at the entry say in wikipedia. Faraday cages are in common use at accelerator labs.
     
  8. Sep 28, 2003 #7

    drag

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    Hmm... So, if I charge a shell with a huge electrical
    charge the sphere, separated by the gap inside, will not
    discharge ? :wink:

    Live long and prosper.
     
  9. Sep 29, 2003 #8

    krab

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    We have a Faraday cage at our lab, which we charge to 300,000 volts. Inside this cage live many power supplies, vacuum pumps, gauges, control system, etc. They operate as normal; there are no sparks jumping from the cage (the shell) to the components inside at any time.

    Rather than provide you with a proof, I urge you to go to

    this link
     
  10. Sep 29, 2003 #9
    So (i read the link, just want to make sure if i understood well).
    If we had a faraday cage, and we did not charge it, but we put it under the effect of an electric field (generated by another object), will the faraday cage still shield its contents from the field generated by the other object ?
    Thanks (this seems interesting).
     
  11. Sep 29, 2003 #10

    krab

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    Yes. The electrons in the metal surface of the cage, since they are mobile, will move until there is no more electric field inside. In this way, they redistribute to exactly cancel the external electric field, for points inside the cage. So even though you did not charge the cage, there is a charge on it, which varies from + at one end, through 0 to - at the other end, and if you add it up over the whole surface you get zero.
     
  12. Sep 30, 2003 #11
    Got it, thanks.
     
  13. Oct 3, 2003 #12

    drag

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    Greetings !
    I'm sorry, but I'm somewhat confused here.
    What exactly do you charge at 300,000 Volts ?
    Also, isn't your Faraday cage earthed ?

    More to the point, in the case mentioned here you
    are not dealing with an external electric field.
    The charge is on the outer shell itself and the inside
    is not hollow but contains a sphere. I do not understand
    why you say that the sphere will no be affected ?
    After all, inside the sphere there must be no electric
    fields, so it must cancel the external electric field
    which will exist at its surface due to its presense
    inside the shell, without which it would of course be 0.
    Am I seriously missing something here ?

    Peace and long life.
     
  14. Oct 3, 2003 #13

    krab

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    drag:
    The Faraday cage is charged to 300 kV. There is a DC power supply between the FC and ground. Other labs have similar setups with 750 kV. These cages are large. One could stay in the cage while it is at voltage, but I don't know of anyone who has done it. A tandem vandegraaff typically runs at 25MV, and the stripping terminal contains many sensitive components that are in no danger from this incredibly high voltage.

    Recall the question from STAii:
    I'm saying that not only can you prove this statement using simple electrostatic laws, but also that it has practical applications which are in daily use.
     
  15. Oct 3, 2003 #14

    drag

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    Greetings !
    What's the voltage for ?
    But this just applies to hollow conductors, doesn't it ?

    Live long and prosper.
     
  16. Oct 3, 2003 #15

    krab

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    It's for accelerating particles. It's a particle accelerator. There is an ion source and guiding optics inside the Faraday cage. This cage has a hole of a few inches in diameter. The optics guides the particles effectively to this hole. Once they experience the electric field at the hole, between the FC and ground, the ions get this whopping big kick so that when they arrive at ground potential, they have an energy of 300keV.
    No. It applies to hollow conductors, solid conductors, metallic shells whose interior is packed solid with a dielectric, whatever. It is immaterial what is inside the metal boundary. The metal boundary shields the contents from electric fields.
     
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