A problem about surface element

[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.

 

[SammyS]

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]

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]

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]

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]

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}\ ?

 

[VHAHAHA]

O, I get what u mean

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

 

[SammyS]

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.