"Qausi-static" displacement current (Purcell)

shooba

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 J_d, he shows that curlJ_d=-(1/4[itex]\pi[/itex]c)(∂²B/∂t²), so that for slowly varying fields, curlJ_d 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 curlJ_d=0 imply B=0?
Thanks!

shooba

Bump? Maybe this belongs in the classical physics section?