24 1. In Cartesian co-ordinates the gradient of a scalar field is given by: მს au VŲ = i +j +k ar ду дz Using r = r cos

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24 1. In Cartesian co-ordinates the gradient of a scalar field is given by: მს au VŲ = i +j +k ar ду дz Using r = r cos 0 and y=r sin o, show that in cylindrical polar co-ordinates, au 1 ay მს Vurur + ar т дф дz where ur, uand uz are the unit vectors in the indicated directions. Hint: Obtain the components in the radial and tangential directions by resolving the Cartesian components, and use the chain rule r, ao to or , up + uz მს au მს to relate de