Discussion
For a flux density \( \mathbf{D} = r^2\mathbf{a}_r \) in spherical coordinates, the charge density is
Answer: A
Correct answer: \( 4r \)
In spherical coordinates the radial divergence carries a metric factor: \[ \nabla\cdot\mathbf{D} = \frac{1}{r^2}\frac{d}{dr}(r^2 D_r) = \frac{1}{r^2}\frac{d}{dr}(r^4) = \frac{4r^3}{r^2} = 4r. \] Differentiating \( D_r \) alone would give \( 2r \), which is the offered trap - the \( r^2 \) must go inside the derivative.
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