# A problem about surface element

by VHAHAHA
Tags: element, surface
 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. Attached Thumbnails
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 Quote by VHAHAHA 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?
P: 58
 Quote by SammyS 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)

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 Quote by VHAHAHA 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 ?
P: 58
 Quote by SammyS 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)?
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 Quote by VHAHAHA 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 $\ \hat{r}\$ in terms of $\ \hat{i},\,\hat{j},\,\hat{k}\ ?$
 P: 58 O, I get what u mean at (0 A 0) , the r is along the y axis, so 0i, 1j , 0k ?
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