Question

Express vector G=ρsinϕaρρcosϕaϕ+ρaz\mathbf{G}=\rho \sin \phi \mathbf{a}_{\rho}-\rho \cos \phi \mathbf{a}_{\phi}+\rho \mathbf{a}_{z} in rectangular coordinates.

Solution

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Answered 1 year ago
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In this task we need to find vector:

G=ρsin(ϕ)aρρcos(ϕ)aϕ+ρaz\begin{aligned} \bold{G}=\rho\sin(\phi)\bold{a_{\rho}}-\rho\cos(\phi)\bold{a_{\phi}}+\rho\bold{a_{z}} \end{aligned}

in rectangular coordinates which is another name for Cartesian coordinates (x,y,z)(x,y,z). We can clearly see that vector G\bold{G} is vector in cylindrical coordinates.

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