Discussion
A flux density of \( \mathbf{D} = 2\rho\,\mathbf{a}_\rho \) C/m² exists in a region. The charge density there is
Answer: B
Correct answer: 4 C/m3
In cylindrical coordinates the radial divergence is \[ \frac{1}{\rho}\frac{d}{d\rho}(\rho D_\rho) = \frac{1}{\rho}\frac{d}{d\rho}(2\rho^2) = \frac{4\rho}{\rho} = 4. \] The metric factor is \( \rho \) here rather than \( r^2 \) as in spherical coordinates, and omitting it would give 2 - the offered trap.
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