- #1
VinnyCee
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Homework Statement
Transform the vector below from Cartesian to Cylindrical coordinates:
[tex]Q\,=\,\frac{\sqrt{x^2\,+\,y^2}}{\sqrt{x^2\,+\,y^2\,+\,z^2}}\,\hat{x}\,-\,\frac{y\,z}{x^2\,+\,y^2\,+\,z^2}\,\hat{z}[/tex]
Homework Equations
Use these equations:
[tex]A_{\rho}\,=\,\hat{\rho}\,\cdot\,\overrightarrow{A}\,=\,A_x\,cos\,\phi\,+\,A_y\,sin\,\phi[/tex]
[tex]A_{\phi}\,=\,\hat{\phi}\,\cdot\,\overrightarrow{A}\,=\,-A_x\,sin\,\phi\,+\,A_y\,cos\,\phi[/tex]
[tex]A_z\,=\,A_z[/tex]
[tex]x\,=\,\rho\,cos\,\phi[/tex]
[tex]y\,=\,\rho\,sin\,\phi[/tex]
The Attempt at a Solution
[tex]Q_{\rho}\,=\,\frac{\sqrt{\left(\rho\,cos\,\phi\right)^2\,+\,\left(\rho\,\sin\,\phi\right)^2}}{\sqrt{\left(\rho\,cos\,\phi\right)^2\,+\,\left(\rho\,\sin\,\phi\right)^2\,+\,z^2}}\,cos\,\phi[/tex]
[tex]Q_{\rho}\,=\,\frac{\rho}{\sqrt{\rho^2\,+\,z^2}}\,cos\,\phi[/tex]
[tex]Q_{\phi}\,=\,-\,\frac{\rho}{\sqrt{\rho^2\,+\,z^2}}\,sin\,\phi[/tex]
[tex]Q_z\,=\,-\,\frac{z\,\rho\,sin\,\phi}{\rho^2\,+\,z^2}[/tex]
Does the above look correct?
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