A problem about surface element

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Homework Help Overview

The discussion revolves around expressing the surface element of a hemisphere in xyz coordinates, contrasting it with the known expression in spherical coordinates. The original poster expresses uncertainty about the conversion and the specific requirements of the problem.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the surface element near a specific point on the hemisphere and question how to express the unit vector in xyz coordinates. There is an exploration of the relationship between spherical and Cartesian coordinates.

Discussion Status

Participants are actively engaging with the problem, questioning the values of angles and the representation of vectors. Some guidance has been offered regarding the unit vector at a specific point, but there remains a lack of consensus on the overall approach to expressing the surface element in the required format.

Contextual Notes

There is a focus on the specific point (0, A, 0) and the implications of converting from spherical to Cartesian coordinates. The discussion highlights the need to adhere to the problem's requirements while navigating the complexities of coordinate transformations.

VHAHAHA
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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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VHAHAHA said:
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.

attachment.php?attachmentid=55804&d=1361038640.png


You say you know the answer in spherical coordinates. What is the answer in spherical coordinates?
 
SammyS said:
That doesn't look very vector-like.

attachment.php?attachmentid=55804&d=1361038640.png


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)
 
VHAHAHA said:
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 ?
 
SammyS said:
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)?
 
VHAHAHA said:
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]
 
O, I get what u mean

at (0 A 0) , the r is along the y axis, so 0i, 1j , 0k ?
 
VHAHAHA said:
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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