a question about Maxwell equation

[Adun]

please refer to the attached picture.
thanks

 

[jallem]

The divergence is roughly a measure of a vector field's increase in the direction it points; but more accurately a measure of that field's tendency to converge on or repel from a point.

Taken from https://en.wikipedia.org/wiki/Del_operator.

In other words, the divergence of J is a measure of how much J change
en la direction given by J itself. Or the solution is the same and there is
no ambiguity.

 

[Adun]

But i think the ambiguity here is between (a) & (b)

(a) Physically, change of coordinate system should NOT change how fast the charge accumulates in a point.
(b) Mathematically, change of coordinate system does seem to change how fast the charge accumulates in a point.

 

[lagrange]

Hi Adun

Being x'y'z' is the rotated system it holds:

x'= -x and (x' versor) = -(x versor)

So you get J =(x' versor) x'

and d(rho)/dt = -5 is not changed by the rotation.

 

[Adun]

thanks lagrange, i just realized my math flaw when i am taking a shower
hail to the maxwell equations