x,y,z), by Sph = {(x, y, z): (x − xo)²+(y - Yo)² + (z - zo)² = a²}, - where a, xo, yo and zo are constants, (0, 0) = (xo + a sin cos , yo + a sin sin , zo + acos #), giving the ranges of ne parameters and p. or the surface Sph, defined in part (a), show that a vector surface element is given y ds a sin 0 [r - (xo, Yo, zo)] dedo, and justify the sign convention associated with this normal vector. Hence evaluate the flux = f = sph f the vector field G = (1, 0, z²) out of the surface. G.dS
x,y,z), by Sph = {(x, y, z): (x − xo)²+(y - Yo)² + (z - zo)² = a²}, - where a, xo, yo and zo are constants, (0, 0) = (xo + a sin cos , yo + a sin sin , zo + acos #), giving the ranges of ne parameters and p. or the surface Sph, defined in part (a), show that a vector surface element is given y ds a sin 0 [r - (xo, Yo, zo)] dedo, and justify the sign convention associated with this normal vector. Hence evaluate the flux = f = sph f the vector field G = (1, 0, z²) out of the surface. G.dS
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(x, y, z), by
in terms of Cartesian coordinates
Sph = {(x, y, z) : (x — xo)² + (y — yo)² + (z − zo)² = a²},
where a, xo, yo and zo are constants,
r(0, ) = (xo + a sin cos , yo + a sine sin d, %0 + a cos), giving the ranges of
the parameters 0 and 6.
=
For the surface Sph, defined in part (a), show that a vector surface element is given
by ds
a sin 0 [r (xo, Yo, zo)] dedo, and justify the sign convention associated
with this normal vector. Hence evaluate the flux
f = = G
#
G.dS
Sph
of the vector field G = (1,0, z²) out of the surface.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3011c556-643e-4a01-b0e0-55d8cf24eddf%2Ffa511da6-be57-496d-8f38-1da69609ae33%2Fer7bt6z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(x, y, z), by
in terms of Cartesian coordinates
Sph = {(x, y, z) : (x — xo)² + (y — yo)² + (z − zo)² = a²},
where a, xo, yo and zo are constants,
r(0, ) = (xo + a sin cos , yo + a sine sin d, %0 + a cos), giving the ranges of
the parameters 0 and 6.
=
For the surface Sph, defined in part (a), show that a vector surface element is given
by ds
a sin 0 [r (xo, Yo, zo)] dedo, and justify the sign convention associated
with this normal vector. Hence evaluate the flux
f = = G
#
G.dS
Sph
of the vector field G = (1,0, z²) out of the surface.
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