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Homework Statement
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.
Homework Equations
$$ P=\int_V \vec r \rho(\vec r)d\tau
$$
The Attempt at a Solution
$$ P=\int_V \vec r \rho(\vec r)d\tau
= \rho_0 \int_0^R \int_0^{2\pi} \int_{-H/2}^{H/2} (r e_{\hat r} + ze_{\hat z}) rdrd\theta dz = 2\pi \rho_0 (\frac {R^3 H} {3}e_\hat r + 0e_{\hat z})
$$