# Cylindrical symmetry, Gauss's Law

1. Feb 16, 2016

### mawgs

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. Feb 16, 2016

### haruspex

That is a reasonable integral to perform, but what exactly do you think it will give you?

3. Feb 16, 2016

### mawgs

Qenc?

4. Feb 16, 2016

### haruspex

Yes. So what is the next step to find the field?

5. Feb 16, 2016

### mawgs

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. Feb 16, 2016

### haruspex

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.

7. Feb 16, 2016

### mawgs

Sorry, I meant epsilon naught.

8. Feb 16, 2016

### haruspex

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