What is the Magnetic Field Around a Thin Walled Circular Conductor?

[Brewer]

Homework Statement

Using Ampere's circuital law, or otherwise, find the magnetic field B a distance r away from the axis of a thin walled circular hollow conductor of radius a and carrying a current I.

Homework Equations

$$\oint_L B\cdot dL = \mu_0I_{enclosed}$$

The Attempt at a Solution

So far I have said:
the conductor is a hoop. As a result inside the hoop (i.e. r<a) B=0 as $$I_{enc}$$=0.

However I am confused as to what line I should take to work out B when r>a. Does the system act like a long straight line (albeit in a circle) and the B-field is a loop around the hoop (cancelling out in the middle, and thus obtaining the same result for r<a), or is it some other shape all together?

 

[chaoseverlasting]

Outside the spherical shell, the magnetic field at a given point is constant. Therefore, $$B\oint dl=\mu_0 I_{enclosed}$$. This would give you $$B=\frac{\mu_0 I_{enclosed}}{4\pi r^2}$$.

 

[Brewer]

Its not a spherical shell is it? I read it as just a circular loop.

I think after a bit of playing with the numbers I get $$B = \frac{\mu_o I}{2\pi r}$$

 

[chaoseverlasting]

How can a circular loop be hollow? As far as I can see, its a spherical shell. However, if it is a circular loop, you would be correct.

 

[Brewer]

It would just be a hoop as opposed to a flat disc.