See attached file for full problem description.
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.© BrainMass Inc. brainmass.com March 4, 2021, 8:05 pm ad1c9bdddf
Please see the attached file for detailed solution.
(A) Cylindrical coordinates:
We define the cylindrical coordinates (r, , z) of a point and we have the following relationships
between rectangular coordinates and cylindrical coordinates:
We have the following relations
Hence the unit vector along the r-direction is
Similarly the unit vector along the -direction is
and the unit vector along the ...
The solution shows how to derive the gradient and divergence formulas in both cylindrical and spherical coordinates in detail.