The magnetic field of an infinite hollow wireWhat happens if we take a wire, drill a hole in it and set some current in motion? Will we encounter a magnetic field?

Problem Statement

The magnetic field of an infinite hollow wire shall be calculated.A wire with radius \(R\) shall carry a constant current density \(j_{0}\). Inside the wire, there is further a hole with radius \(a<R\)  which is displaced in \(x\) direction relative to the center of the with a certain distance \(d\). So, the current density may be described by\[\begin{eqnarray*} \mathbf{j}\left(\mathbf{r}\right)&=&\begin{cases}j_{0} & \text{inside the wire}\\0 & \text{in the hole and outside}\end{cases}  \end{eqnarray*}\]and the hole by \(\left\{ \mathbf{r}:\ \sqrt{\left(x-d\right)^{2}+y^{2}}\leq a\right\} \).

Find the magnetic field inside of the hole.

You may regard our result from the problem "Magnetic Field of an Infinite Wire" as given. 

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