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Homework Help: Computing Work

  1. Oct 21, 2008 #1
    1. The problem statement, all variables and given/known data
    Convert F into cartesian coordinates from spherical
    F = -4*theta*e_r + 1e_phi
    r(t) = 2, theta(t) = 4t, phi(t) = pi / 2
    2. Relevant equations
    x = rsin(theta)cos(phi)
    y = rsin(theta)sin(phi)
    z = rcos(phi)

    3. The attempt at a solution
    Where I'm having problem is converting F into Cartesian coordinates.
    Last edited: Oct 21, 2008
  2. jcsd
  3. Oct 21, 2008 #2


    Staff: Mentor

    What do e_r and 1e_phi mean in this equation?
    F = -4*theta*e_r + 1e_phi
  4. Oct 22, 2008 #3
    e_r and e_theta are the unit vectors... for the coordinate system I believe.

    [tex]\hat{e_{r}}[/tex] and [tex]\hat{e_{\theta}}[/tex]
  5. Oct 22, 2008 #4


    Staff: Mentor

    You have an error in your conversion formulas, at least if you're using theta and phi in their usual meanings. The formulas should be:
    x = rho* sin(phi)*cos(theta)
    y = rho*sin(phi)*sin(theta)
    z = rho*cos(phi)

    Compare the formulas for x and y with the ones you have in your first post. Phi is the angle between the z-axis and the vector to the point (rho, theta, phi). If you project this vector onto the x-y plane, you get a vector of length r, where r = rho*sin(phi). Theta is the angle between this projected vector and the x-axis.

    Haven't run into the unit vectors e_r and e_phi before. Since they're unit vectors, their magnitutes must be 1. What about their directions? I would guess that e_r (really e_rho) is a unit vector with the same direction as the vector from the origin to the point (rho, theta, phi). Is that correct? I can't picture what direction e_phi points if it's some direction other than the direction for e_rho. Can you provide definitions for these unit vectors?
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