(a) (b) (c) r(u, v) = (u cos v, u sin v, v); u € [0, 2], v € [0, π]. (*) Find r, and r. (**) Calculate ru x rv. to S? i Cos v -u sin v = sin vi- cos vj + uk ru xrv = det j sin v u cos v k 0 1, (**) What is the total charge on the surface S if the surface charge density is given by restricting the function o(x, y, z)=√x² + y²
(a) (b) (c) r(u, v) = (u cos v, u sin v, v); u € [0, 2], v € [0, π]. (*) Find r, and r. (**) Calculate ru x rv. to S? i Cos v -u sin v = sin vi- cos vj + uk ru xrv = det j sin v u cos v k 0 1, (**) What is the total charge on the surface S if the surface charge density is given by restricting the function o(x, y, z)=√x² + y²
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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Need help with part c). Please explain each step and neatly type up. Thank you :)
![8. Let S be a parametric surface
(a)
(b)
(c)
r(u, v) = (u cos v, u sin v, v); u = [0, 2], v = [0, π].
(*) Find ru, and rv.
(**) Calculate ru x rv.
to S?
i
cos v
-u sin v
= sin vi- cos vj + uk
ru x rv = det
j
sin v
u cos v
(**) What is the total charge on the surface S if the surface charge
density is given by restricting the function
o(x, y, z) =
=
k
0
1
x² + y²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fe1fc35-672a-49fd-831b-9642c77888ed%2F75f237ff-eb4f-4dd5-a07e-b2f5c9ed042e%2Fwm5nbky_processed.png&w=3840&q=75)
Transcribed Image Text:8. Let S be a parametric surface
(a)
(b)
(c)
r(u, v) = (u cos v, u sin v, v); u = [0, 2], v = [0, π].
(*) Find ru, and rv.
(**) Calculate ru x rv.
to S?
i
cos v
-u sin v
= sin vi- cos vj + uk
ru x rv = det
j
sin v
u cos v
(**) What is the total charge on the surface S if the surface charge
density is given by restricting the function
o(x, y, z) =
=
k
0
1
x² + y²
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