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Math Help - Gradient, divergence and curl - nabla dotted with f(r)r

  1. #1
    Senior Member chella182's Avatar
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    Gradient, divergence and curl - nabla dotted with f(r)r

    Sorry for the naff title, couldn't think of anything else. I've ended with a ridiculous answer...

    a) Find \nabla\cdot\left(f(r)\mathbf{r}\right), where r=|\mathbf{r}|, \mathbf{r}=(x,y,z) and f is a differentiable function.

    b) In Part (a), find f(r) such that \nabla\cdot\left(f(r)\mathbf{r}\right)=0.

    I ended up with something like \frac{df}{dr}r+3f(r) for part a), which I highly doubt is right thus I can't really attempt part b)... cheers in advance.
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  2. #2
    Senior Member
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    So far so good

    You're right on part a. Why don't you try this for part (b)?
    <br />
f(r) = \frac {1}{r^3}<br />

    This will be very useful when you think about vector fields that go like <br />
\frac {1}{r^2} such as electric fields.
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