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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

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    (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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