Magnetic Forces in and around a coaxial cable

[032050]

Homework Statement

So I'm doing a problem set and the question refers to a coaxial cable, I am told that the cable consists of an inner solid cable radius (R₁), which is surrounded by a outer thin tube with radius (R²) , both have the same current though them but opposite direction. I have to create equations for the magnetic field inside the inner cable, between the two, and outside the tube. The picture I am given is a filled in circle inside of a larger circle.
My questions about doing the problem are:
1. Should the thin tube be modeled as a solenoid? But then I don't know the number of turns
2. If I use Amperes Law, then wouldn't I get a I_through of zero?

Homework Equations

magnetic field inside a current carrying wire is =[(µIr)/2piR²]

The Attempt at a Solution

Honestly I don't even know where to start because I don't know how to model the outer circle

 

[tiny-tim]

welcome to pf!

hi 032050! welcome to pf!

(have a mu: µ and try using the X² and X₂ icons just above the Reply box )

1. Should the thin tube be modeled as a solenoid? But then I don't know the number of turns

no …

there's no turns …

if you like, you can model it as a million very thin wires running along the tube, each with one-millionth of the current

 

[032050]

Thanks, so if I model the outer tube using Ampere's Law to calculate the I_through wouldn't that give zero current and then zero magnetic field?

 

[tiny-tim]

maybe …

where? ​

 

[032050]

ohhh..
is it inside the wire I would only use the current component of the inner wire, between the two I would still only use the inner wire, and then outside i would add the two to get Ithrough=0?

 

[tiny-tim]

yup!

 

[032050]

Thankyouuuu!