MHB How Do You Calculate the Normal Vector of a Sphere in Spherical Coordinates?

[brunette15]

I am given the sphere V= x^2 + y^2 + z^2 =< 1

I have converted it to spherical coordinates:

x = rsin(t)cos(f)
y = rsin(t)cos(f)
z = rcos(t)

where t ranges from 0 to pi, and f ranges from 0 to 2pi.

I am unsure how to go about this problem from here. Any guidance would be really appreciated :)

 

[I like Serena]

I am given the sphere V= x^2 + y^2 + z^2 =< 1

I have converted it to spherical coordinates:

x = rsin(t)cos(f)
y = rsin(t)cos(f)
z = rcos(t)

where t ranges from 0 to pi, and f ranges from 0 to 2pi.

I am unsure how to go about this problem from here. Any guidance would be really appreciated :)

Hey brunette15! ;)

We can find the normal of a surface $f(x,y,z)=0$ by taking the gradient $\nabla f$... (Thinking)

 

[brunette15]

Hey brunette15! ;)

We can find the normal of a surface $f(x,y,z)=0$ by taking the gradient $\nabla f$... (Thinking)

Hi again I like Serena :)

I am aware that we could do that but for this particular case i am trying to prove the divergence theorem of Gauss :/

 

[I like Serena]

Hi again I like Serena :)

I am aware that we could do that but for this particular case i am trying to prove the divergence theorem of Gauss :/

Huh?

What do you want to do then?

Do you want to find the normal in polar coordinates?
If so, the method is the same - we just need the gradient in polar coordinates instead of cartesian coordinates.