Question

The divergence of the curl of a vector field is:

• A. the magnitude of this vector field
• B. the argument of this vector field
• C. the magnitude of the curl of this vector field
• D. zero

Hint:

The divergence of the curl of any vector field is always zero. This property is frequently used in electromagnetism and fluid dynamics.

Answer 1

The Correct Option is D

In vector calculus, one of the fundamental identities states that the divergence of the curl of any vector field is always zero. Mathematically, it is expressed as: \[ \nabla \cdot (\nabla \times \mathbf{F}) = 0 \] This means that for any vector field \( \mathbf{F} \), when you take the curl of the field and then calculate the divergence of that curl, the result is always zero. This identity holds for all types of vector fields, including those found in fluid dynamics, electromagnetism, etc. Hence, the correct answer is option (D) zero.