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The magnetic field Im(dz/z) is irrotational 
The derivative lenses, and the curl-lens clearly showed that the magnetic field Im(dz/z) is irrotational (derivative criterion). But the meaning of irrotational becomes most obvious when comparing how solid regions move in the skew-symmetric part of the linearized flow of this field with how they move in the harmonic oscillator (“never see the back side of the moon”) -- i.e., when considering the associated differential equations.

 

Slide 16 of 18