A second problem:::

[bluesky]

For static field and finite currents, div A=0.I did this problem in the following manner,whereas everywhere else I found the problem done in a different way.Please tell me if I am wrong...

div.A=(mu/4pi) int{div.(J(r')/|r-r'|)} dV'

People generally change div to -div' here and proceed by product rules...

I applied the divergence theorem directly to get---

div.A= -(mu/4pi) int{div'.(J(r')/|r-r'|)} dV' = -(mu/4pi) closed int{J (r')/|r-r'|)}.da'

 

The last is the same integral that the other elaborate method yields as the final step...

This is zero because over the closed surface a', either J is inside or, tangential

[sanctus]

I don't see why you shouldn't be allowed to use the divergence theorem...