# Cylindrical symmetry, Gauss's Law

## 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?

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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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?

Qenc?

haruspex
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Gold Member
Qenc?
Yes. So what is the next step to find the field?

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.

haruspex
Homework Helper
Gold Member
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.

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.

haruspex