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# Gradient and divergence formulas

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Derive the gradient formula for a potential in both cylindrical and spherical coordinates. Also, derive the divergence formula of the vector field in both coordinates.

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https://brainmass.com/physics/scalar-and-vector-operations/gradient-divergence-formulas-143528

#### Solution Preview

Please see the attached file for detailed solution.

(A) Cylindrical coordinates:
(a) gradient:
We define the cylindrical coordinates (r, , z) of a point and we have the following relationships
between rectangular coordinates and cylindrical coordinates:
(1)
We have the following relations
(2)
Hence the unit vector along the r-direction is
(3)
Similarly the unit vector along the  -direction is
(4)
and the unit vector along the ...

#### Solution Summary

The solution shows how to derive the gradient and divergence formulas in both cylindrical and spherical coordinates in detail.

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