General form of a central force isF(r)=F(r) (r^)

[Note that This form of central force satisfiesL=rxp=0 as well]

But the isotropic or centro-symmetric form is

F(r)=F(r) (r^)

I found in a book that the second form of a central force is conservative.OK,this can be proved easily.What about the first expression?It is NOT centro-symmetric...depends on the position vectorrit is acting on.

Why is it NOT conservative always?

Actually,I am not sure whether the same curl operation will do...Please check it...I am getting stuck in the differentiation of the r vector wihin the bracket while taking the curl.I feel confusion if the curl in two cases can be done in exactly similar way.