1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dipole moment of a cylinder

  1. Nov 10, 2014 #1
    1. The problem statement, all variables and given/known data
    I am trying to calculate the dipole moment of a cylinder of volume charge density ##\rho_0## of radius ##R## and height ##H## with is center coinciding with the origin. My guess is that it should be 0 because of the symmetry but I am not able to show it. Below is my calculation attempt. Thanks for any help.

    2. Relevant equations
    $$ P=\int_V \vec r \rho(\vec r)d\tau
    $$
    3. The attempt at a solution
    $$ P=\int_V \vec r \rho(\vec r)d\tau
    = \rho_0 \int_0^R \int_0^{2\pi} \int_{-H/2}^{H/2} (r e_{\hat r} + ze_{\hat z}) rdrd\theta dz = 2\pi \rho_0 (\frac {R^3 H} {3}e_\hat r + 0e_{\hat z})
    $$
     
  2. jcsd
  3. Nov 15, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. Nov 15, 2014 #3

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Hello.
    Looks like you are treating the unit vector ##\hat{e}_r ## as a constant vector in the integration. Does it have the same direction throughout the cylinder?

    What is the meaning of ##\hat{e}_r ## in your final answer? What direction does this ##\hat{e}_r ## point?

    Can you express ##\hat{e}_r ## at a point in the cylinder in terms of ##\hat{e}_x ##, ##\hat{e}_y ##, and ##\theta##? Would this help?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Dipole moment of a cylinder
  1. Dipole moment (Replies: 8)

  2. Dipole Moment (Replies: 3)

  3. Dipole Moments (Replies: 1)

  4. Dipole Moment (Replies: 1)

Loading...