Question on current flux

Question

I found this in Jack Vanderlinde's Classical Electromagnetic Theory, Problem 1-13:
"A fine needle emits electrons isotropically at a steady rate. Find the divergence of the current density and the resulting current flux at distance r from the point in the steady state."
Now, for the divergence of the current density, I figured it's about continuity equation, and the value is $-frac{partial rho}{partial t}$ at any distance from the needle. But i don't understand about current flux; what did the question ask, or what current flux even mean.

jensen paull · Answer

current density flux is zero in this case as it is a steady current. current density is a VECTOR FIELD  and like any other vector field it can have a divergence. this intuatively mean , given you have a pillbox drawn ( gaussian surface) around some current density. its surface integral must be zero... aka, the same amount of charge remains inside this box at all times
and yes, it directly relates to the continuity equation. in integral form the continuity equation is :
the closed surface flux  integral  of J = -d/dt of the volume integral of charge density .
where the  closed surface  encloses the volume

Question on current flux

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