I was looking at the formula for divergence in cylindrical system and couldn't quite understand the existence of a certain term . So the divergence in cylindrical system is gives as
$\nabla .\vec A = \dfrac{\partial Ap}{\partial p} + \dfrac {Ap} {p} + \dfrac{1}{p}\dfrac{\partial{A\theta}}{\partial{\theta}}+\dfrac{\partial Az}{\partial z}$
Existence of all the terms are self-explanatory except $\dfrac{Ap}{p}$ . Why is that term needed . I know it arrives during the derivation but what is the meaning of that term ?
Thank you
$A_{\rho}$ is the component of $A$ along $\hat{\rho}$. So the term $\frac{A_{\rho}}{\rho}$ is simply that component over $\rho$.
If you understand the derivation, you understand that that term is needed. If you want the divergence in only three terms, you have
$$\nabla \cdot A=\frac{1}{\rho}\frac{\partial (\rho A_{\rho})}{\partial \rho}+\frac{1}{\rho}\frac{\partial A_{\theta}}{\partial \theta}+\frac{\partial A_z}{\partial z}$$