Discussion
Consider the following statements about vector fields. 1. The curl of a gradient vanishes identically 2. A solenoidal field has a vector potential 3. Every field with zero curl has zero divergence
Answer: D
The first two are standard. The third confuses the two conditions: the radial field \( x\mathbf{i} + y\mathbf{j} + z\mathbf{k} \) is irrotational yet has divergence three. The two properties are independent, and a field satisfying both is the special harmonic case
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