Discussion
The divergence of \( \mathbf{A} = \rho \, \mathbf{a}_\rho \) in cylindrical coordinates is
Answer: D
Correct answer: 2
\[ \nabla\cdot\mathbf{A} = \frac{1}{\rho}\frac{\partial}{\partial\rho}(\rho A_\rho) = \frac{1}{\rho}\frac{\partial}{\partial\rho}(\rho^2) = \frac{2\rho}{\rho} = 2. \] The \( \rho \) must go inside the derivative; differentiating \( A_\rho \) alone would give 1, which is the offered trap.
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