Magnetic Field Problem (Wire within a Tube)

[loto]

Well, I was going through some example problems to study for a test and came upon one I can't figure out. Here is the question:

A long straight cylindrical tube has an inner radio Ri and an outer radius Ro. It carries a current i, uniformly distributed over its cross section. A wire which runs along the tube axis carries a current of the same magnitude but opposite in direction.

The magnetic field created by these currents is:
A. zero outside the tube, but non-zero elsewhere
B. zero inside the tube, but non-zero elsewhere
C. zero everywhere
D. zero outside the tube and in the conducting material of the tube, but nonzero inside the tube
E. non-zero everywhere

I really should know this, but seem to be having a brain fart. Since the currents are opposite, the magnetic fields will be opposite in direction but equal in magnitude. Now, I would think this would mean that the field would be zero inside the tube and non-zero elsewhere, but something seems wrong with that.

Any hints would be greatly appreciated!

 

[Doc Al]

Consider Ampere's Law. This arrangement has cylindrical symmetry, so the field at any radius from the center can be easily related to the total current passing through a circle with that radius.

 

[loto]

Ahh, I understand. If the radius of the Amperian loop is less than the outer radius of the tube, the enclosed current will not equal zero. However, as soon as the radius of the loop is greater than that of the outer edge of the tube the two equal enclosed currents will negate each other and there will be no field.

At least, I think I understand. Thank you very much.

 

[Doc Al]

Sounds like you've got it.