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SarkariResultOutBMS · 2024

Previous Year Question

For a static magnetic field, the following statements are givenStatement 1:It is solenoidal.Statement 2:It is conservative.Choose the correct option for the above statements
  1. Statement 1 is true, but statement 2 is false
  2. Both statements 1 and 2 are false
  3. Statement 1 is false, but statement 2 is true
  4. Both statements 1 and 2 are true

Correct answer: A

Explanation

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.

Formula

∇·B=0; ∇×H=J

Step-by-step solution

Solenoidal but Not Generally Conservative explanatory diagram

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.

Common mistake

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

Exam tip

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

Quick method

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