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The curl of the gradient of the scalar field defined by V = 2x²y³z² + 4z²x is

1. 4xy aₓ + 6yz a_y + 8zx a_z
2. 4 aₓ + 6 a_y + 8 a_z
3. [4xy + 4z²] aₓ + [2x² + 6yz] a_y + [3y² + 8zx] a_z
4. 0

Correct answer: 0

Solution

The curl of the gradient of any scalar field is always zero, as it represents the rotational component of a conservative vector field, which has no rotation.

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