Finding E Field at Point from non uniform charge density

In summary, using cylindrical coordinates, we can determine the electric field in free space at point P(0,0,4) due to a non-uniform charge density of 10|z| (nC/m) along the z-axis where |z| < 2. The correct expression for the position vector is R = (4-z)az and the resulting electric field is 34.20 az (V/m).
  • #1
fmpak93
9
0
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.

Homework Equations


E = (1/4πε0) ∫ dQ*aR/(R2)

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).
I
 
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  • #2
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
TSny said:
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?

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
fmpak93 said:
Thus making our vector R = (4-|z|)az. Is this correct?

No. Should R be the same for z = +2 and z = -2?
 
  • #5
TSny said:
No. Should R be the same for z = +2 and z = -2?

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

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

Related to Finding E Field at Point from non uniform charge density

1. What is the formula for finding the electric field at a point from a non-uniform charge density?

The formula for finding the electric field at a point from a non-uniform charge density is given by E = (1/4πε0) ∫(ρ(r') (r-r') / |r-r'|^3) dτ, where ρ(r') represents the charge density at a particular point and r represents the distance between the point of interest and the point of charge.

2. How does the electric field vary with distance from a point charge in a non-uniform charge distribution?

The electric field varies with distance from a point charge in a non-uniform charge distribution because as the distance increases, the amount of charge within a particular region decreases, resulting in a decrease in the electric field strength.

3. Can the electric field at a point be negative in a non-uniform charge distribution?

Yes, the electric field at a point can be negative in a non-uniform charge distribution. This occurs when the direction of the electric field is opposite to the direction of the electric force on a positive charge.

4. What factors affect the strength of the electric field at a point from a non-uniform charge distribution?

The strength of the electric field at a point from a non-uniform charge distribution is affected by the amount of charge present, the distance between the point of interest and the point of charge, and the distribution of charge in the surrounding area.

5. How can the electric field at a point from a non-uniform charge distribution be visualized?

The electric field at a point from a non-uniform charge distribution can be visualized using field lines, where the direction of the field is indicated by the direction of the lines and the density of the lines represents the strength of the field. Another way is by creating a graph of the electric field strength versus distance from the point of charge.

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