How is E Calculated in a Coaxial Cable with Alternating Current?

[Kolahal Bhattacharya]

Homework Statement

An alternating current I cos wt flows down a long wire and returns along a coaxial conducting tube of radius a. Find E assuming E→0 at ∞.

Homework Equations

The Attempt at a Solution

I did the problem from Griffiths but have some problem to understand the physical situation. I did using ∫E∙dl = (-dΦ/dt) and proceeded straight away as B=μn I cos wt.
How much it is justified as I am simply neglecting the current returning through the conducting tube?

 

[Meir Achuz]

B comes from Ampere's law, which includes only the current within the loop.
The current in the outer tube is outside the loop.

 

[Kolahal Bhattacharya]

How do you know where to construct Ampere's loop?At first you are to justify that the B field must be 0 outside the tube.

 

[Meir Achuz]

Ampere's loop is a circle within the tube, where you need to know B.
The field outside the tube ils irrelevant.