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Help with Feynman's math!

  1. Feb 8, 2004 #1
    Hi everyone,

    I'm reading Feynman's "Lectures on Physics" and I'm stuck on one little part. If any of you out there have the books, I'm on pg. 70 of Vol. II of the 3 volume set.

    Can someone tell me how Eq. 6.12 is equal to cos(theta) = z/r?

    I'll lay out the problem below.

    The section is about the electric field due to a dipole, but I don't think a knowledge of the physics is necessary to clear up the problem I'm having. I understand everything conceptually, but there's a mathematical quirk which I can't explain to myself.

    The electric potential (psi) is defined as: [p*cos(theta)]/r^2

    where: p = dipole moment (q*d)
    cos(theta) = distance along axis of dipole (z) over distance from
    center of dipole to point P in question (r)
    = z/r
    r = magnitude of vector r
    q = magnitude of each charge in dipole
    d = distance between the two charges of the dipole

    Mr. Feynman goes on to "vectorize" p by giving it the magnitude of p (defined above) and direction going from the negative charge to the positive charge.

    The part I don't understand is, he redefines cos(theta) = z/r as cos(theta) = vector p (dotted with) direction vector e along length r. How does he arrive at that??

    Thanks in advance for all your help.
  2. jcsd
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