- #1
teme92
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- 2
Homework Statement
Evaluate the force corresponding to the potential energy function ##V (r) = \frac{cz}{r^3}##, where ##c## is a constant. Write your answer in vector notation, and also in spherical polars, and verify that it satisfies ##∇∧F = 0##.
Homework Equations
##F(x)=-\frac{dU}{dx}##
Spherical Coordinates:
##r=\sqrt{x^2+y^2+z^2}##
The Attempt at a Solution
[/B]So I'm confused a bit here. I think the vector notation will only have a ##z## component. So differentiate to get ##F## and then as ##r## is a polar coordinate I just change ##r^3## to ##\sqrt{x^2+y^2+z^2}^3##. This doesn't look right though. I have a list of relations from cartesian to spherical coordinates but I don't understand how to answer the question with the ##\frac{1}{r^3}##. I know how to do the last bit which is the curl. Thanks in advance for any help in the right direction.