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Cylindrical symmetry, Gauss's Law

  1. Feb 16, 2016 #1
    1. The problem statement, all variables and given/known data

    A semiconducting nanowire has a volume charge density ρ(r)=ρ0(r/R) where R is the radius of the nanowire. How would you calculate the electric field inside the wire?

    2. Relevant equations

    Gauss's Law

    3. The attempt at a solution

    I know that by symmetry the E field only points radially out. Using Gauss's law and finding the dq by integrating in terms of dr, a small ring in the gaussian cylinder. So would you integrate ρ0(r/R)2piLdr from 0 to r?
     
    Last edited: Feb 16, 2016
  2. jcsd
  3. Feb 16, 2016 #2

    haruspex

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    That is a reasonable integral to perform, but what exactly do you think it will give you?
     
  4. Feb 16, 2016 #3
    Qenc?
     
  5. Feb 16, 2016 #4

    haruspex

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    Yes. So what is the next step to find the field?
     
  6. Feb 16, 2016 #5
    Set the Qenc over E0 equal to E2πrL. When I did this, I got ρ0r/E0R. I know this is wrong because the homework is online and gives instant feedback. When I integrated, I got .5(2πρ0Lr)/R. I'm not sure where I went wrong.
     
  7. Feb 16, 2016 #6

    haruspex

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    Sorry, what's E0? Sounds like a field. Why would you divide the charge by a field?
    You haven't taken into account the charge between r and R.
     
  8. Feb 16, 2016 #7
    Sorry, I meant epsilon naught.
     
  9. Feb 16, 2016 #8

    haruspex

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    Ok. But I think you lost a factor of 2 in there somewhere.
     
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