Question
Wed December 14, 2011 By: Aditi Priya
 

Expression of magnetic field along axis of solenoid of finite length

Expert Reply
Wed December 14, 2011
magnetic fld along the axis of solenoid is ?0nI ,where n=number of turns/length.
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.
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