Just as the capacitor can be constructed to create a uniform electric field between the plates with zero field outside the region bounded by the plates, so too the long solenoid gives rise to a uniform magnetic field throughout the interior region and an exterior field that is zero. This can be seen by probing the field not only as a function of axial position but of radius as well. For the finite length solenoid, the on-axis interior field designated by H_
in Fig. 8.2.4 is given by (13) for locations on the z
axis where d/2 z
In the limit where the solenoid is also very long compared to its radius, where d/2a 1, this expression becomes
Probing of the field shows the field maintains the value and direction of (16) over the interior cross-section as well.
the magnetic field intensity just outside the windings at an axial location that is several radii a from the coil ends is relatively small.