(d) State the expression for the divergence of Fin cylindrical polar coordi- nates and evaluate for given above. (e) State the expression for the curl of F in cylindrical polar coordinates and evaluate for F given above.
(d) State the expression for the divergence of Fin cylindrical polar coordi- nates and evaluate for given above. (e) State the expression for the curl of F in cylindrical polar coordinates and evaluate for F given above.
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D and E needed
Transcribed Image Text:2) Consider
and
F(r, o, z) = ² + 2res +5r² zez
²0
223
(a) What are the Lamé coefficients for cylindrical polar coordinates?
(b) State the expression for the gradient of in cylindrical polar coordinates
and evaluate forgiven above.
(c) State the expression for the Laplace operator acting on in cylindrical
polar coordinates and evaluate for given above.
(d) State the expression for the divergence of Fin cylindrical polar coordi-
nates and evaluate for given above.
v=
(e) State the expression for the curl of F in cylindrical polar coordinates and
evaluate for F given above.
Note: You may make use of the following formula for a general curvilinear
coordinate system if you need to:
V.F=
² =
V
1
hy h₂h3
VX
1 d
h₁ Oqi
1 მა 1 მ
·e₂+
h₂ 892
h3 dq3
[Ə(h₂h3F1)_(h₂h3F2)+ a(hyh₂ F3)
მq2
993
hie hae haes
d
8
8
eit
091
1
hihaha
+
1
Ә
მს
hiliahs (Don (de)
hahaha
aq |მი2 ags
F1 F₂h2 F3h3
8
hy h₂ d
243 ha aq
-e3.
+
ə
842
(his de)
მს
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