- #1

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## Homework Statement

Text description: Let V(z) be the potential of a ring of charge on the axis of symmetry at

distance z from the center. Obtain the first two non-vanishing terms of the multipole expansion

for V(z) with z>>a where a is the radius of the ring. Can you see by symmetry that the dipole moment is

zero?

My issue: While I was able to do the monopole term just fine. The problem is with the dipole

moment term. My work (outlined below) keeps giving me a positive term, however intuition

and the geometry of the problem (as well at the text's statement of the problem)

dictate that the dipole moment is zero. Can anyone point out where I went wrong in my work?

2. Homework Equations

a)Definition of the Electric Dipole Moment for a continuous body

##\vec p(\vec{x'})=\int \vec{x'} \lambda {dx'}##

b)My Setup

##\vec p(\vec{x'})=\lambda a^2 \int_{0}^{2\pi}\hat{s}{d\phi'}##[/B]

## The Attempt at a Solution

The following is the result I have gotten to thus far.

[/B]

##\vec p(\vec{x'})={2\pi}\lambda a^2\hat{s}##