Discussion
Match the property with the field it describes. 1. Solenoidal 2. Irrotational 3. Both at once P. Expressible as a gradient Q. Expressible as a curl R. Its potential satisfies Laplace's equation
Answer: B
A divergence-free field is the curl of a vector potential, since every curl is solenoidal. A curl-free field is the gradient of a scalar, since every gradient is irrotational. A field with both properties has \( \nabla \cdot \nabla\phi = 0 \), so its scalar potential is harmonic
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