Discussion :: Exam Questions Paper
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Consider the following diagrams showing vector fields :
The correct statements are
|
A.
For figure (a), ∇ .
 = 0, ∇ x = 0 |
|
B.
For figure (a), ∇ .
= 0, ∇ x ≠ 0 |
|
C.
For figure (b), ∇ .
= 0, ∇ x ≠ 0 |
|
D.
For figure (c), ∇ .
= 0, ∇ x ≠ 0 |
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Answer : Option B
Explanation :
In figure
Fx = 0 hence div F = ∇ . = 0, but curl F ≠ 0.
In figure
magnitude of F remains constant and hence ∇ . = 0 and also it is possible that ∇ . = 0, as there can be an electrostatic field in which 
and circulation around any closed path in it may be equal to zero.
In Figure
has a central field (radial).
∴ ∇ x = 0, ∇ ≠ 0.
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