Magnetic field of a wire current surrounded by an aluminum tube

[FishStik]

Magnetic field inside infinitely conductive hollow tube

Homework Statement

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)?

Homework 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

The Attempt at a Solution

My initial guess was that the infinitely conductive tube has no effect on the magnetic field induced by the current-carrying wire, and the magnetic field can be calculated for the two different wire locations as if the tube was not there. Is this correct, or does the presence of the tube change the induced magnetic field in some way?

Thanks in advance.

 

[maajdl]

When the wire is moved, this induces an electric current in the cylinder.
This current will never disappear since the tube is a perfect conductor.

 

[utkarshakash]

When the wire is moved, this induces an electric current in the cylinder.
This current will never disappear since the tube is a perfect conductor.

Why is a current induced in the tube?

 

[maajdl]

http://en.wikipedia.org/wiki/Lenz's_law

That's exactly why a dynamo produces current (or emf).

 

[HalfLostAndSearching]

I would like to clarify that the infinitely conductive tube will not have any effect on the magnetic field induced by the current-carrying wire. This is because the tube has an infinite conductivity, meaning that it will have no resistance to the flow of current and will not create its own magnetic field. Therefore, the magnetic field at x=15cm will remain the same regardless of the wire's position.

However, it is important to note that if the tube had a finite conductivity, it could potentially affect the magnetic field due to the presence of eddy currents. These eddy currents would create their own magnetic field, which would interact with the magnetic field of the wire and potentially alter it. In this case, the magnetic field at x=15cm would change when the wire is moved to (x,y)=(0,0).

In conclusion, the infinitely conductive tube will not change the magnetic field induced by the current-carrying wire, but a finite conductivity could potentially affect it due to the presence of eddy currents.