Cylindrical Gaussian Surface around charged rod

[Mnemonic]

Homework Statement

a) 21.4-nC of charge is placed on a 4.8-m long steel tube with a d = 5.9-cm diameter. What is the magnitude of the electric field as a radial distance of r = d / 3?

b) What is the magnitude of the electric field as a radial distance of r = 20 d?

I was able to determine the answer to b) using Gauss's law however I don't know how to determine the answer to a) as the gaussian surface cylinder appears to be smaller than rod it is meant to surround.

Homework Equations

Φnet=∫ E.dA
ξ0Φ=q(enclosed)
ξ0 is meant to mean epsilon nought

The Attempt at a Solution

For part b):
Surround the rod with a gaussian cylinder of length (l) 6.3 metres and radius (r) 20*0.059

Flux on end caps are zero so:
Φnet=∫ E.dA
=E*2*Pi*r*l

ξ0Φ=q(enclosed)

Rearrange for E=q/(2Pi*r*lξ0)This gives me the E for part b)

For part a I tried the same method but with radius=1/3*0.059

Is this correct?

I also considered the fact that since the Gaussian Field is smaller than the charged object the Electric field would equal zero as all the charge is on the surface of the object.

What am I missing?

 

[Orodruin]

This is not a very well defined question. Are you supposed to assume that the charge is evenly distributed on the tube? This will not actually happen since steel is a conductor and the charge distribution will be unevenly distributed. Since I assume the tube is hollow, there is no charge inside it and there would not be even if it was a solid cylinder (again, since steel is a conductor).