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The divergence of \( \mathbf{D} = 3x\mathbf{a}_x + 2y\mathbf{a}_y \) gives a charge density of

  • A.6 C/m³
  • B.1 C/m³
  • C.\( 3x + 2y \)
  • D.5 C/m³

Answer: D

Differentiating each component with respect to its own coordinate and adding gives \( 3 + 2 = 5 \), a uniform density throughout the region. A z component would add a third term, and its absence simply means nothing depends on z.

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