Mathematics Exam > Mathematics Questions > Ifthenisa)irrotationalb)solenoidalc)scalard)N...
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If 
then 
is
then is- a)irrotational
- b)solenoidal
- c)scalar
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Ifthenisa)irrotationalb)solenoidalc)scalard)None of theseCorrect answe...
Correct Answer :- a
Explanation : curl F = ∇ × F
= (∂/∂x, ∂/∂y, ∂/∂z) × (F1, F2, F3)
(∂F3/∂y − ∂F2/∂z , ∂F1/∂z − ∂F3/∂x , ∂F2/∂x − ∂F1/∂y)
= (∂z/∂y − ∂y/∂z , ∂x/∂z − ∂z/∂x, ∂y/∂x − ∂x/∂y)
= (0, 0, 0)
Note that since this curl is 0, the radial vector field
F(x, y, z) = (x, y, z) is irrotational.
Most Upvoted Answer
Ifthenisa)irrotationalb)solenoidalc)scalard)None of theseCorrect answe...
Correct Answer :- a
Explanation : curl F = ∇ × F
= (∂/∂x, ∂/∂y, ∂/∂z) × (F1, F2, F3)
(∂F3/∂y − ∂F2/∂z , ∂F1/∂z − ∂F3/∂x , ∂F2/∂x − ∂F1/∂y)
= (∂z/∂y − ∂y/∂z , ∂x/∂z − ∂z/∂x, ∂y/∂x − ∂x/∂y)
= (0, 0, 0)
Note that since this curl is 0, the radial vector field
F(x, y, z) = (x, y, z) is irrotational.
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Ifthenisa)irrotationalb)solenoidalc)scalard)None of theseCorrect answer is option 'A'. Can you explain this answer?
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