Qausi-static displacement current (Purcell)

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The discussion centers on Purcell's explanation of "quasi-static" displacement current and its effect on magnetic fields in slowly varying fields. It highlights that the curl of the displacement current, represented as curlJd, is nearly zero, leading to the conclusion that there is no magnetic field generated in such conditions. The confusion arises regarding how curlJd=0 directly implies that the magnetic field B is also zero. Participants are encouraged to clarify this relationship and whether the topic fits better in classical physics discussions. Understanding this concept is crucial for grasping the implications of displacement current in electromagnetic theory.
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"Qausi-static" displacement current (Purcell)

Hello all,
On page 329, chapter 9 of Purcell's E&M book, he describes why the "displacement current" produces nearly zero magnetic field for slowly varying fields. By taking the curl of the displacement current Jd, he shows that curlJd=-(1/4\pic)(∂2B/∂t2), so that for slowly varying fields, curlJd is nearly zero. From this, using a symmetry/superposition argument he concludes that there can be no magnetic field for such a current distribution. It is this last step that I do not understand; how does curlJd=0 imply B=0?
Thanks!
 
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Bump? Maybe this belongs in the classical physics section?
 

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