(d) The vector field F has the form F(r) g(r)a, where g(r) is an arbitrary differentiable scalar field and a is a constant vector. Use index notation to express curl F in terms of grad g. Hence, by applying Stokes's theorem to the field F, show that fg dr = - / / 7 g x ds. Vgx dS, with S a smooth open orientable surface bounded by the simple closed curve C. You may assume the scalar triple product rule bxc.d=b.cx d if vectors b, c and d are not operators.
(d) The vector field F has the form F(r) g(r)a, where g(r) is an arbitrary differentiable scalar field and a is a constant vector. Use index notation to express curl F in terms of grad g. Hence, by applying Stokes's theorem to the field F, show that fg dr = - / / 7 g x ds. Vgx dS, with S a smooth open orientable surface bounded by the simple closed curve C. You may assume the scalar triple product rule bxc.d=b.cx d if vectors b, c and d are not operators.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![(d) The vector field F has the form F(r) g(r)a, where g(r) is an arbitrary
differentiable scalar field and a is a constant vector. Use index notation to express
curl F in terms of grad g. Hence, by applying Stokes's theorem to the field F,
show that
£gdr = - ] [ 7g x ds.
Vgx
with S a smooth open orientable surface bounded by the simple closed curve C.
You may assume the scalar triple product rule b × c.d=b .cx d if vectors b, c
and d are not operators.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69cce4ac-4bf6-4e6b-8636-bf160e045b58%2F205b3ec6-48e3-4f18-b36f-776aea93af29%2Fxoebjyi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(d) The vector field F has the form F(r) g(r)a, where g(r) is an arbitrary
differentiable scalar field and a is a constant vector. Use index notation to express
curl F in terms of grad g. Hence, by applying Stokes's theorem to the field F,
show that
£gdr = - ] [ 7g x ds.
Vgx
with S a smooth open orientable surface bounded by the simple closed curve C.
You may assume the scalar triple product rule b × c.d=b .cx d if vectors b, c
and d are not operators.
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