An infinitely long uniform solid wire of radius a carries a uniform DC current of density J.
A hole of radius b (b < a) is now drilled along the length of the wire at a distance d from the center of the wire. The magnetic field inside the hole is
(A) uniform and depends only on d
(B) uniform and depends only on b
(C) uniform and depends on both b and d
(D) non uniform
Figure source: https://qph.ec.quoracdn.net/main-qimg-951b32724c2858cd9823dcf535fbd49a
As far as my approach goes, the progress I made is:
a) I used Ampere's circuital law to find field B at a point P when the hole didn't exist.
By using it, $H 2\pi R = J\pi R^2$, where $R$ is the distance from the origin to a point P.
b) Now, once the hole is drilled, a part of the cross section becomes hollow. I wonder how to approach the problem from hereon.
Will the hollow portion be able to have any current flowing through it ? If no, there won't be any magnetic field inside it. But, the options clearly don't suggest such a possibility.
Can a hollow portion of a wire support any current? The possibility doesn't seem logical, but if there's no current in the hollow portion, how can there be a magnetic field at a point within it? Maybe it is due to the current in the rest of the solid cross section. I would like a clarification in this regard.
