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B Electric field by continuous charge distributions.

  1. May 2, 2017 #1
    While reading the book, Electricity and magnetism, the author says that electric field just outside a spherical shell is ##4\pi \sigma##, on it ##4\pi\sigma r_0^2## ,inside is ##0## and outside is ##Q/R^2##.

    My derivations :-

    For inside,

    ##E\Delta S = 4\pi Q = 0## since ##Q = 0##.

    For outside,

    ##E \Delta S = 4 \pi {Q} \iff E \cdot 4 \pi R^2= 4 \pi {Q} ##

    For just outside,

    ##E \cdot (4\pi r_0^2) = 4\pi \sigma (4\pi r_0^2)##.

    But I am unable to derive the one for "on it", any suggestions what should I do ?

    So far I get,

    ##E \cdot (\Delta S) = 4\pi (\sigma 4\pi r_0^2)##.

    What should be ##\Delta S## ?

    Note for future readers :-

    The charge is ##4\pi\sigma r_0^2## not the Field. I read it incorrectly.
     
    Last edited: May 2, 2017
  2. jcsd
  3. May 2, 2017 #2

    Charles Link

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    Homework Helper
    Gold Member

    It looks like the author is using cgs units, where ## E=Q/r^2 ##. Meanwhile "on it", refers to the charge ## Q ## that is "on it", ## Q=(4 \pi r_o^2) \sigma ##. ## \\ ## Editing... Additionally ## E=4 \pi \sigma ## at ## r=r_o ## (i.e. ## r ## just slightly greater than ## r_o ##.)
     
  4. May 2, 2017 #3
    Yes you are correct. It my mistake, he meant charge on it is ##4\pi r^2_0\sigma## not the electric field.

    Thanks and sorry for this useless question :((.
     
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