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The curl of the gradient of the scalar field defined by V = 2x² y³ z² + 4z² x 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 rotation of a conservative vector field, which has no curl.

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