Grappling with a Magnetism question

[sharpstones]

When analyzing a coaxial cable and trying to find the B field in the space between the outer and inner cables, using ampere's law the B field will be depedent only upon the current running through the inner wire.

Why is this? I know that yes Ampere's law says that only the current contained within the amperean loop can cause a B field, but i want a better explanation then that. Let's suppose there was just a plain hollow cylindrical conductor with current running through it. Would there be a B field running through it?

 

[Gokul43201]

The better explanation is in writing the field due to several elemental sections of the conductor, using Biot-Savart's Law and integrating over the entire conductor. Unfortunately, it's a mathematical explanation, not a physical demonstration.

The only physical thing that can be said (this amy seem obvious) is that the contributions from different parts of the conductor cancel each other out in the case of say, the hollow conductor. So, the answer to that part is "No, there will be no field inside a hollow cylindrical conductor".

To answer the first part, the B-field is not dependent on only the current. It is also dependent, in this case, on the radial distance of the particular point.

 

[sharpstones]

regarding the first part. I wasn't very specific... what I ment was that i was suprised to find that it was dependent upon the curreny on the inner wire, but non dependent at all on the outer concentric wire.