Question

The curl of a vector field \( F \) is zero throughout a region of space. What does this imply about the behavior of \( F \)?

• A. The field \( F \) is solenoidal.
• B. The field \( F \) is irrotational.
• C. The field \( F \) is conservative.
• D. The field \( F \) is neither solenoidal nor irrotational.

Hint:

The curl of a vector field gives a measure of the rotationality of the field; zero curl indicates that the field is irrotational.

Answer 1

The Correct Option is B

If the curl of a vector field is zero, it implies that the field is irrotational, meaning the field has no rotational component at any point in the region. A conservative field also has zero curl, but the primary distinction is that it can be expressed as the gradient of a scalar potential.