- #1
maggie56
- 30
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Homework Statement
Hi,
i am trying to find the div, grad and curl in cylindrical polar coordinates for the scalar field
[tex] \ phi = U(R+a^2/R)cos(theta) + k*theta [/tex] for cylindrical polar coordinates (R,theta,z)
I have attempted all three and would really appreciate it if someone could tell me if the answers look ok as I am really not sure whether i have correctly followed the method
Thank you
Sorry i forgot to put that its the curl of the gradient and divergence of the gradient that I am finding. I guess i have a non zero answer for curl of gradient because U,a and k are constants so my answer would be zero for certain U,a,k.
Homework Equations
[tex] \ phi = U(R+a^2/R)cos(theta) + k*theta [/tex] U,a,k constants
The Attempt at a Solution
For gradient of phi [tex] \ U(1-a^2/R^2)cos(theta) [/tex] R'hat' - [tex] \[ U(1+a^2/R^2)sin(theta) + k/R] [/tex]
theta'hat'
Curl of phi [tex] \ sin(theta)(2Ua^2/R^4 + U/R - a^2/R^3) - k/R^3 [/tex] z'hat'
divergence of phi is zero
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