Curl of current density

In summary, the curl of current density is a mathematical operation that describes the rotational aspects of the current flow in a given region of space. It is used in electromagnetism to relate the distribution of electric currents to the magnetic fields they generate, as expressed in Maxwell's equations. The curl of the current density vector indicates how the current circulates around a point, providing insights into the behavior of magnetic fields and the dynamics of charge movement in conductive materials. This concept is crucial for understanding phenomena such as electromagnetic induction and continuity equations in physics.
  • #1
fluidistic
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Hello, I have derived an expression for ##\vec J## in a particular, unusual physical problem in 2D. The expression is different from ##\vec 0## everwhere in the material except at at least two different points.

Can I conclude that the only way for this to occur is that ##\vec J## itself decays to ##\vec 0## the closer it gets to the center of the vortices? I assume that the current density vanishes exactly at the center of vortices of currents.

Also, what can I conclude about the magnetic field?
 
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  • #2
Would you be able to share the expression or perhaps have an image?

I would assume that the magnetic field decays to zero since at those vortices the current goes to zero.
 
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