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SarkariResultOutBMS · 2024

Previous Year Question

Given the following statementsStatement 1:The curl of a vector field is another vector field.Statement 2:The divergence of the curl of a vector field is zero.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: D

Explanation

The curl of a vector field is itself a vector field. In any sufficiently smooth field, the vector identity ∇·(∇×A)=0 holds identically. Therefore both statements are correct and option D applies.

Formula

∇·(∇×A)=0

Step-by-step solution

Divergence of Curl Identity explanatory diagram

Correct Answer

D — Both statements 1 and 2 are true

Statement-wise Analysis

Statement 1: True

Statement 2: True

Concept and Reasoning

The curl of a vector field is itself a vector field. In any sufficiently smooth field, the vector identity ∇·(∇×A)=0 holds identically. Therefore both statements are correct and option D applies.

Calculation / Key Relation

∇·(∇×A)=0

Exam Takeaway

Divergence of any curl is zero.

Common Mistake

Do not confuse this identity with curl of a gradient, ∇×(∇V)=0; both are valid but different identities.

Common mistake

Do not confuse this identity with curl of a gradient, ∇×(∇V)=0; both are valid but different identities.

Exam tip

Divergence of any curl is zero.

Quick method

Divergence of any curl is zero.