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A problem about surface element

by VHAHAHA
Tags: element, surface
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VHAHAHA
#1
Feb16-13, 12:17 PM
P: 58
I really don't know how to do this question as it asks me to write the surface element of a hemisphere in xyz coordinates. I know how to answer if it is asked in spherical coordinates.

I think this is a tricky question because it asks for the portion da near (0, A, 0) (in xyz) where A is the radius.

I guess da = dydz.
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SammyS
#2
Feb16-13, 12:37 PM
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Quote Quote by VHAHAHA View Post
I really don't know how to do this question as it asks me to write the surface element of a hemisphere in xyz coordinates. I know how to answer if it is asked in spherical coordinates.

I think this is a tricky question because it asks for the portion da near (0, A, 0) (in xyz) where A is the radius.

I guess da = dydz.
That doesn't look very vector-like.



You say you know the answer in spherical coordinates. What is the answer in spherical coordinates?
VHAHAHA
#3
Feb16-13, 12:38 PM
P: 58
Quote Quote by SammyS View Post
That doesn't look very vector-like.



You say you know the answer in spherical coordinates. What is the answer in spherical coordinates?
it should be r^2sin(θ)dθdϕ (unit vector r)

SammyS
#4
Feb16-13, 12:41 PM
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A problem about surface element

Quote Quote by VHAHAHA View Post
it should be r^2sin(θ)dθdϕ (unit vector r)
What is the value of θ at (x,y,z) = (0,A,0) ? ... the value of r ?
VHAHAHA
#5
Feb16-13, 12:45 PM
P: 58
Quote Quote by SammyS View Post
What is the value of θ at (x,y,z) = (0,A,0) ? ... the value of r ?
it is equal to 90 degree or pi/2
so i should plug this valve to the expression?
i have tried but the question needs me to express it in xyz coor,
how to deal with (unit vector of r)?
SammyS
#6
Feb16-13, 12:57 PM
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Quote Quote by VHAHAHA View Post
it is equal to 90 degree or pi/2
so i should plug this valve to the expression?
i have tried but the question needs me to express it in xyz coor,
how to deal with (unit vector of r)?
At the point, (0,A,0), what is [itex]\ \hat{r}\ [/itex] in terms of [itex]\ \hat{i},\,\hat{j},\,\hat{k}\ ?[/itex]
VHAHAHA
#7
Feb16-13, 01:14 PM
P: 58
O, I get what u mean

at (0 A 0) , the r is along the y axis, so 0i, 1j , 0k ?
SammyS
#8
Feb16-13, 01:43 PM
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Quote Quote by VHAHAHA View Post
O, I get what u mean

at (0 A 0) , the r is along the y axis, so 0i, 1j , 0k ?
Just put this with dydz.


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