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    Hi, can someone please explain this to me.
    I have the vector field
     \mathbf{v}=\mathbf{r}=\dfrac{ \hat{r}}{r}.

    Taking the divergence using Spherical Polar Coordinates gives me
     \boldsymbol{\nabla}\cdot\mathbf{  v}=\dfrac{1}{r^2},

    however, if I convert this to cartesian coordinates I get the divergence to be 3. What is going on here?
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    (Original post by KeyFingot)
    Hi, can someone please explain this to me.
    I have the vector field
     \mathbf{v}=\mathbf{r}=\dfrac{ \hat{r}}{r}.

    Taking the divergence using Spherical Polar Coordinates gives me
     \boldsymbol{\nabla}\cdot\mathbf{  v}=\dfrac{1}{r^2},

    however, if I convert this to cartesian coordinates I get the divergence to be 3. What is going on here?
    You need to check your working for the cartesian case - I think you may have made the mistake of thinking that \hat{r}/r = (x,y,z) in cartesian coordinates, which isn't the case (but would give a divergence of 3).
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    (Original post by Mark13)
    You need to check your working for the cartesian case - I think you may have made the mistake of thinking that \hat{r}/r = (x,y,z) in cartesian coordinates, which isn't the case (but would give a divergence of 3).
    Oh I see now, cheers
 
 
 
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