# Finding E Field at Point from non uniform charge density

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1. Feb 22, 2015

### fmpak93

1. Portion of z-axis for which |z| < 2 carries a non uniform charge density of 10|z| (nC/m). Using cylindrical coordinates, determine E in free space at P(0,0,4). Explicitly show your integration.

2. Relevant equations
E = (1/4πε0) ∫ dQ*aR/(R2)

3. The attempt at a solution
https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-xpf1/v/t34.0-12/11004892_945246908827650_417954135_n.jpg?oh=d538ef93ebc53d426c29d8a2f0116327&oe=54ECD699&__gda__=1424795396_496617364f01c6d9bac875a291ef70af
I don't know what I'm doing wrong. the linear charge lies on the z axis and the point of interest lies on (0,0,4) so only the z unit vector applies right? As shown in the paper, the real answer is E = 34.20 az (V/m).
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2. Feb 22, 2015

### TSny

Welcome to PF!

Everything looks good except for your expression for $\vec{R}$. Try evaluating your expression for z = +2 and z = -2. Does it make sense?

3. Feb 22, 2015

### fmpak93

I would assume the R vector we can find as the difference in points between the source and destination. So our destination point is P(0,0,4), and our source charge point would have to be (0,0,|z|). Thus making our vector R = (4-|z|)az. Is this correct?

4. Feb 22, 2015

### TSny

No. Should R be the same for z = +2 and z = -2?

5. Feb 22, 2015

### fmpak93

Oh I see, it shouldn't. The absolute factor only applies to the charge density, the length of the position vector will still vary from top to bottom like always. So then just R = (4-z)?

6. Feb 22, 2015

### fmpak93

Never-mind, you were right. I got the answer. THANKS! :)