Solenoidal but Not Generally Conservative

Correct Answer

A — Statement 1 is true, but statement 2 is false

Statement-wise Analysis

Statement 1: True

Statement 2: False

Concept and Reasoning

Magnetic flux density is solenoidal because ∇·B=0—there are no magnetic monopoles. A static magnetic field is not generally conservative in regions containing current, since Ampère’s law gives ∇×H=J. Therefore statement 1 is true and statement 2 is false, matching option A.

Calculation / Key Relation

∇·B=0

∇×H=J

Exam Takeaway

Magnetic B is always divergence-free; H may have curl where current exists.

Common Mistake

Do not apply the electrostatic condition ∇×E=0 directly to magnetostatic H in a current-carrying region.