Abstract
A widespread assertion has existed for a long time, believing the external field of an infinitely long solenoid should be zero, but it is proofed to be wrong in this work. The components of magnetic flux density of current-carrying, closely wound cylindrical solenoids are calculated. At a distant field point, the external field definitely has a nonzero component, being equal to that of a straight wire of equal length. Since this equivalence is length-independent, it still holds true for ideal solenoids having infinite length. Hence the incorrect and still spreading inference about long solenoids should be rectified. Furthermore, theoretical and experimental discussions involving solenoids should be reviewed again carefully.
Highlights
Scientific research related to magnetic field has a long history [1] [2], and covers a wide range of fields [3]
Since adequate discussions have been made for solenoids with finite length, it is possible to infer the results for a very long solenoid
It has been verified that, no matter how long the solenoid is, the BX of its external field always equals that of a straight wire having an equal length and carrying an equal current
Summary
Scientific research related to magnetic field has a long history [1] [2], and covers a wide range of fields [3]. It is believed that the external magnetic field generated by an infinitely long, closely wound, current-carrying ideal cylindrical solenoid is zero [4]. This inference is used as a basic knowledge in further studies, such as the early research works related to the Aharonov-Bohm effect [1] [2]. The calculated field approaches that of an infinitely long solenoid. In this extreme case, the field distribution at distant points turns out to be exactly the same as that of an infinite straight wire
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