# Help with Feynman's math!

1. Feb 8, 2004

### precar

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??