Magnetism derivation

[bluesky]

Griffiths writes:

 

A®=(mu/4pi) int{(1/|r-r'|) [del' x M(r')]}dV'+(mu/4pi) closed int{(1/| r-r'|) [M(r') x da']}

Then in next step,he has replaced del' x M by del x M to define J_b

I have referred to the chapter of dielectrics and polarization where also I noticed a parallel approach to define rho_b

Discussion with friends and other books suggests that we may omit the prime on the del that operates on M,since that del clearly operates on x',y',z' of the point where magnetization is M.

But, I am hesitating to accept this explanation as we have dealt with cases where del x a vector quantity depending on primed co-ordinates is equal to zero.Like del x J(r')=0 in magnetostatics to prove div B=0 from Bio-Savart's law.

 

Is it that: J_b®=del x M® in general

and J_b(r')=del' x M(r') ?