# Magnetic field at the centre of a cable that has an offset hole

1. Nov 16, 2011

### JNBirDy

1. The problem statement, all variables and given/known data
[From Electromagetism by I. S. Grant & W. R. Phillips, Q4.7]

A cable of circular cross-section & diameter 0.2 m has a long cylindrical hole with a diameter of 0.001 m drilled in it parallel to the cable axis. The distance between the axis of the hole and cable axis is 0.005 m. The cable has a uniform steady current density of 10$^{5}$A/m$^{2}$ flowing in it, determine the magnetic field at the centre of the cable.

Answer: ∏ x 10$^{-6}$ Tesla

2. Relevant equations

Ampere's Law

3. The attempt at a solution

I know that to find the magnetic field I need to calculate the magnetic field of the cylinder carrying the current density and then add to the field of a current density -J in the opposite direction that would be occupying the hole. I've come up with the equation:

B = μ/2 * J * (r$_{1}$ - r$_{2}$) where r$_{1}$ is the distance from the axis of the main cylinder to the centre of it and r$_{2}$ is the distance from the axis of the hole to the centre of the main cylinder. However this gives me an answer of ∏ x 10$^{-4}$ T when I use r$_{1}$ = 0.01 m and r$_{2}$ = 0.005 m.

What am I doing wrong? Any help is appreciated.