A charge -3.2 micro-coulombs is spread evenly throughout a rod of length (a). At a distance (b) from the rod, what is the electric field?
a = 1.2 m
b = 3.4 m
So basically, you start at zero and then there's a line of charge horizontally to the right from 0 to 1.2 meters, and then at 3.4 meters to the right of the origin there is a point that is distance b away from the end of (a), and I need to find the electric field there.
E = kq/r^2
charge density = dq/dx
The Attempt at a Solution
I used E = kq/r^2
I knew that the charge density = dq/dx
So I set up the integration like this: E = integral(k/r^2)dq
Then I switched to terms of dx... E = integral((k * charge density)/r^2)dx
Then I plugged in 3.4 + x for r... E = integral((k * charge density)/(3.4 + x)^2)dx
k and the charge density were constants for I pulled the out of the integral and integrated 1/(3.4+x)^2dx from 0 to 1.2. I did used u substitution to do this.
I was wondering if I used the correct method here, and if my answer was correct.
I got -1840 N/C