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I know the divergence of any position vectors in spherical coordinates is just simply 3, which represents their dimension. But there's a little thing that confuses me.

The vector field of A is written as follows,

,

and the divergence of a vector field A in spherical coordinates are written as follows

, which shows you have to put terms of A related to theta or psi.

However, when you represent a position using a position vector in spherical coordinates, you usually only use r hat simply because r hat includes angle terms already.

Then, when do you use theta or psi terms? And what exactly do A_theta and A_psi term represent when r hat already has the meaning of angles? I have a feeling that they are redundant.

I heard this is related to something called spherical symmetry but wanna understand it strictly. Thanks!

The vector field of A is written as follows,

and the divergence of a vector field A in spherical coordinates are written as follows

However, when you represent a position using a position vector in spherical coordinates, you usually only use r hat simply because r hat includes angle terms already.

Then, when do you use theta or psi terms? And what exactly do A_theta and A_psi term represent when r hat already has the meaning of angles? I have a feeling that they are redundant.

I heard this is related to something called spherical symmetry but wanna understand it strictly. Thanks!

**[Moderator's note: Approved as not being homework.]**
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