# Magnetic field of a wire current surrounded by an aluminum tube

**1. The problem statement, all variables and given/known data**

There exists a thin-walled hollow aluminum tube (assume σ=∞) of radius 10 cm centered around the z-axis. A long wire with 5 mm radius has a total current 2 mA in the z-direction and is centered initially at x=-5cm as shown. How does the magnetic field at x=15cm change if the wire is moved to (x,y)=(0,0)?

**2. Relevant equations**

Magnetic field of an infinitely long current-carrying wire:

[itex]\Large\overrightarrow{B}=\frac{\mu _oI}{2\pi r}[/itex]

where:

μ_{o} is the permeability of free space

I is the current in the wire

r is the distance away from the wire

**3. The attempt at a solution**

What I don’t know is if the infinite conductivity of the hollow tube affects the magnetic field induced by the current-carrying wire. My initial guess was that it has no effect, and the magnetic field can be calculated for the two different wire locations as if the tube is not there. But after reading about the Meissner effect and superconductors’ expulsion of magnetic field, I’m not sure if the tube would contain the magnetic field within itself. If this is true, then obviously the magnetic field would be zero at x=15cm regardless of the wire’s location within the tube. So, which, if any, line of thinking is correct on this one?

Thanks in advance.

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