- #1
renegade05
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Homework Statement
So the full problem reads: A vector F has the same magnitude and direction at all points in space. Choose the z-axis parallel to F. Then , in Cartesian coordinates, [tex]\vec{F}=F\hat{z}[/tex], where [tex]\hat{z}[/tex] is the unit vector in the z direction. Express [tex]\vec{F}[/tex] in spherical coordinates.
Homework Equations
I don't know?
The Attempt at a Solution
Well pretty much it wants me to express this vector field that is parallel with the z-axis, which really means converting [tex]\hat{z}[/tex] to spherical coordinates.
I found the answer to be [tex]\hat{z} = cos(\phi)\hat{r}-sin(\phi)\hat{\phi}[/tex] through an online resource I really didn't understand. No images, nothing. Can someone please explain how you can convert the unit vectors to spherical?
And would the answer be [tex]\vec{F}=F\hat{z} = F(cos(\phi)\hat{r}-sin(\phi)\hat{\phi})[/tex]
thanks!