- #1
2019
- 6
- 0
Hey, I've been stuck on this question for quite a while now:
1a. Write down an expression for the position vector r in spherical polar coordinates.
1b. Show that for any function g(r) of r only, where r = |r|, the result [itex]\nabla[/itex] x [g(r)r] = 0 is true. Why does this imply that there is a potential function associated with any vector field g(r)r?
So for (1a) I've written r = r[itex]\hat{e}[/itex][itex]_{r}[/itex]
But for (1b) I really don't know what I'm doing, I know how to take the curl but not which function to use. So could anyone give me a clue as to where to start?
For the potential function bit I've written about the vector field being path-independent.
Thanks
Homework Statement
1a. Write down an expression for the position vector r in spherical polar coordinates.
1b. Show that for any function g(r) of r only, where r = |r|, the result [itex]\nabla[/itex] x [g(r)r] = 0 is true. Why does this imply that there is a potential function associated with any vector field g(r)r?
Homework Equations
The Attempt at a Solution
So for (1a) I've written r = r[itex]\hat{e}[/itex][itex]_{r}[/itex]
But for (1b) I really don't know what I'm doing, I know how to take the curl but not which function to use. So could anyone give me a clue as to where to start?
For the potential function bit I've written about the vector field being path-independent.
Thanks
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