Guass Law involving conducting cylinders

[maiad]

Homework Statement

Two coaxial cylindrical conductors are shown in perspective and cross-section above. The inner cylinder has radius a = 2.0 cm, length L = 10.0 m and carries a total charge of Qinner = + 8.0 nC (1 nC = 10-9 C). The outer cylinder has an inner radius b = 6.0 cm, outer radius c = 7.0 cm, length L = 10.0 m and carries a total charge of Qouter = - 16.0 nC (1 nC = 10-9 C). What is Ex, the x-component of the electric field at point P which is located at the midpoint of the length of the cylinders at a distance r = 4.0 cm from the origin and makes an angle of 30.0o with the x-axis?

https://www.smartphysics.com/Content/Media/Images/EM/IE/cylinderx/coaxial.gif

Homework Equations

E A= q(enclosed)/$\epsilon$

The Attempt at a Solution

I simply treated the enclosed charge as +8nC, but I've seen ppl using linear charge density and yet they still got the answer. Is just just fluke luck that i got the answer? This is an online hmwk grading system btw.

 

[Doc Al]

I simply treated the enclosed charge as +8nC, but I've seen ppl using linear charge density and yet they still got the answer. Is just just fluke luck that i got the answer?

No, it's not a fluke. You are to assume that this section of length L is just a piece out of a much longer cable (or you are looking only at the field near the center of the piece). The field is cylindrically symmetric, so the length you choose to analyze doesn't matter.

Regardless of how you choose to solve it, if you use Gauss's law you'll need the charge enclosed in whatever Gaussian surface you use. That charge can be thought of as λL, where λ is the linear charge density. Note that L drops out of your final answer.