## divergence and curl of vector field defined by \vec A = f(r)vec r

1. The problem statement, all variables and given/known data
A vector field is defined by A=f(r)r
a) show that f(r) = constant/r^3 if $$\nabla$$. A = 0
b) show that $$\nabla$$. A is always equal to zero

2. Relevant equations
divergence and curl relations

3. The attempt at a solution
I tried using spherical co-ordinates to solve this. But I am not sure if i am totally right.

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 Recognitions: Gold Member Homework Help I would also use spherical coordinates on this problem. I cannot say if you are right since I haven't seen any of your work. I'll need to see some work if you want more specific advice.

Recognitions:
Homework Help
 Quote by FourierX 1. The problem statement, all variables and given/known data A vector field is defined by A=f(r)r a) show that f(r) = constant/r^3 if $$\nabla$$. A = 0 b) show that $$\nabla$$. A is always equal to zero 2. Relevant equations divergence and curl relations 3. The attempt at a solution I tried using spherical co-ordinates to solve this. But I am not sure if i am totally right.
Certainly parts (a) and (b) can not be consistent as you have written them... i suppose part (b) should be a curl not a divergence?

## divergence and curl of vector field defined by \vec A = f(r)vec r

here is what i've done and where i got stuck:

$$\nabla$$A = $$\frac{1}{r^{2}}$$ $$\frac{\partial}{\partial r} (r^{2}f(r))$$

on simplifying this i got:

f(r) = $$\frac{-1}{2} r f'(r)$$

then i integrated with a hope to get an expression for f(r) but did not end up with what i needed i.e. f(r) = constant/ r^{3}

 Recognitions: Homework Help Science Advisor Well the way you interpreted it, you have $$\mathbf{A}=f(r)\hat{r}$$, but the way the question is stated it is $$\mathbf{A}=f(r)\mathbf{r}=$$, or $$\mathbf{A}=f(r)r\hat{r}$$. This extra factor of r should give the answer required.

 Tags curl, divergence, vector