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wellmax
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Homework Statement
I have a vector field (which happens to be a magnetic field)
H = -[itex]\frac{I }{2 \pi r}[/itex]u[itex]\varphi[/itex]
u[itex]\varphi[/itex] is the unit vector
which is in the cylindrical coordinate system with only the [itex]\varphi[/itex] component nonzero so it circles around the z-axis. r is the radius of the circle.
the question is: write H in the cartesian coordinate system.
Homework Equations
i already know the answer through common sense but I'm not able to derive it myself:
H = [itex]\frac{-I}{2 \pi \sqrt{x^2+y^2}}[/itex][[itex]\frac{y}{\sqrt{x^2+y^2}}[/itex] - [itex]\frac{x}{\sqrt{x^2+y^2}}[/itex]]
The Attempt at a Solution
now I know these relations:
x = r Cos[[itex]\varphi[/itex]]
y = r Sin[[itex]\varphi[/itex]]
r = [itex]\sqrt{x^2+y^2}[/itex]
but i can't produce the answer with these
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