# Uniform Linear Charge

1. Sep 28, 2009

1. The problem statement, all variables and given/known data
A nonconducting rod of length L = 8.15cm has charge -q = -4.23 fC uniformly distributed along its length. What are the magnitude and direction [relative to the positive direction of the x axis] of the electric field produced at point P, a distance a = 12.0cm from the rod?

NOTE: In the illustration, the rod and P are along the x axis, and P is to the right of the rod (assumed to be the positive end).

2. Relevant equations
dE = dq/(4*pi*E0*r2)
dq = Lambda*dx
E0 = permeativity of free space = 8.85x10-12
Lambda = linear charge density = q/L

3. The attempt at a solution
I am not sure how 'L' and 'a' are to replace 'r' in the equation above. I have tried r = L + a, but it seems this method does not correctly describe the situation. I then tried to integrate the equation along the limits from 0 to L, but am not sure how to include the additional distance of 'a' into the equation. This seems like a fairly simple question, but my text does not extensively pursue this topic.

2. Sep 28, 2009

### willem2

what you have to compute is $$\int_0^L \frac {dq} { 4 \pi \epsilon_0 r^2}$$

where r = the distance from the charge element dq to the point P