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Vector in cylindrical polar coordinates

  1. Apr 20, 2004 #1
    The problem is:

    Write the vector V=i+j+k=(1,1,1) at the point (x,y,z)=(1,1,1) in cylindrical polar coordinates. What is the gradient of the function phi=x(x^2+y^2)z at this point?

    Answer:

    I don't know how to write the vector in cylindrical polar coordinates. I know that the coordinates are (r(perpendicular), theta, z). Can someone show me how to do this in cylindrical polar coordinates with an example?

    Is the gradient of the funcition 4i+2j+2k at (1,1,1)?
     
  2. jcsd
  3. Apr 20, 2004 #2

    turin

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    Homework Helper

    The vector components in cylindrical polar coordinates depend on position. The position can be expressed in cylindrical polar coordinates as:

    (ρ,θ,z)

    where ρ is the perpendicular distance from the Cartesian z-axis, θ is the angle about the Cartesian z-axis that a line connecting the point to the Cartesian z-axis would make from the Cartesian x-axis, and z is the Cartesian z-coordinate. The Cartesian components of a vector transform into the cylindrical polar coordinates of a vector as:

    vρ = (√(ux2+uy2))cos(θ-arctan(uy/ux))
    vθ = -(√(ux2+uy2))sin(θ-arctan(uy/ux))
    vz = uz

    where

    v = uxex+uyey+uzez = vρeρ+vθeθ+vzez




    That's what I got.
     
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