Answer to Question #112853 in Electricity and Magnetism for mimi

Question

find gradient of scalar fields

W = 2p (z^2 + 1) cos Φ

Answer 1

$\nabla W=\nabla (2\rho (z^2 + 1) \cos \phi)$

$\nabla W=2 (z^2 + 1) \cos \phi e_{\rho}+4\rho z\cos \phi e_{z}\\-\left(\rho^{-1}\right)2\rho (z^2 + 1) \sin \phi e_{\phi}$

$\nabla W=2 (z^2 + 1) \cos \phi e_{\rho}+4\rho z\cos \phi e_{z}\\-2 (z^2 + 1) \sin \phi e_{\phi}$