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Cylindrical symmetry, Gauss's Law

  • Thread starter mawgs
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Homework Statement


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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?

Homework Equations



Gauss's Law

The Attempt at a Solution


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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?
 
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Answers and Replies

  • #2
haruspex
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would you integrate ρ0(r/R)2piLdr from 0 to r?
That is a reasonable integral to perform, but what exactly do you think it will give you?
 
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Qenc?
 
  • #5
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Yes. So what is the next step to find the field?
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.
 
  • #6
haruspex
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Set the Qenc over E0 equal to E2πrL.
Sorry, what's E0? Sounds like a field. Why would you divide the charge by a field?
I know this is wrong
You haven't taken into account the charge between r and R.
 
  • #7
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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.
Sorry, I meant epsilon naught.
 
  • #8
haruspex
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Sorry, I meant epsilon naught.
Ok. But I think you lost a factor of 2 in there somewhere.
 

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