Current density and vector potential

[oddiseas]

Homework Statement

What current density would produce the vector potential
A(r)=(-kmu/2pi)In(r/a) (in the z direction)

where k is a constant, in cylindrical coordinates?

Homework Equations

The Attempt at a Solution

i have done this three times and i get zero current density.So i am wondering if i am making a mistake, there is only one component for A the z component so when i use B=grad*A, i get a field in the fita direction, then when i use J=(grad*B)/mu i get zero.

 

[gabbagabbahey]

Homework Statement

What current density would produce the vector potential
A(r)=(-kmu/2pi)In(r/a) (in the z direction)

where k is a constant, in cylindrical coordinates?

Homework Equations

The Attempt at a Solution

i have done this three times and i get zero current density.So i am wondering if i am making a mistake, there is only one component for A the z component so when i use B=grad*A, i get a field in the fita direction, then when i use J=(grad*B)/mu i get zero.

Hint: \frac{r}{r} is undefined at r=0