Take a long cylinder of radius $ a$.
It has a long cylindrical hole of radius $b$ parallel to the cylinder axis.
The distance between the two axes is $d$. If the cylinder has a uniform current density of $J$, calculate the magnetic field at the centre of the cable, and at the centre of the hole.
I understand this to be a problem involving superposition. I have managed to calculate the magnetic field in the hole to be $ \frac{\mu_0 Jd}{2} $
I am confused how to get the magnetic field at the centre of the cylinder. I thought to calculate the magnetic field of the whole cylinder without a hole, and the subtract from that my answer for the magnetic field in the hole i.e.:
$B_{net} = B_{cylinder} – B_{hole} $
but this does not give me the answer i expect.
Any help is appreciated. Thank you
Best Answer
Consider the hole as just another cylinder with opposite current density of the same absolute value which compensates the current density field of the large cylinder within the hole.
When you have understood this concept apply superposition of the B-fields.
One hint: The answer is maybe much simplier than you expect and this is directly related to the cylinder axes and to the B-field of a symmetric circular-cylindrical conductor in dependence of the radius (as distance from the axis).