# 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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#### 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.