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Gavroy
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I am calculating the dipole moment of a metal sphere in a uniform electric field E_0 in z-direction. From here I know that the charge density [look at page 15][1]
http://www.phy.iitb.ac.in/~dkg/PH-102/conductors.pdf[/PLAIN]
is given by 3 \epsilon_0 E_0 cos(\theta)
Now I wanted to calculate the resulting dipole moment by \int_0^R \int_0^{2\pi} \int_0^{\pi} r^3 sin(\theta) cos(\theta) 3 \epsilon_0 E_0 d\phi d\theta dr
but in this case the integral over \theta is zero and therefore this whole term will be zero which is somewhat strange, since there should be a dipole moment. So what am I doing wrong?
http://www.phy.iitb.ac.in/~dkg/PH-102/conductors.pdf[/PLAIN]
is given by 3 \epsilon_0 E_0 cos(\theta)
Now I wanted to calculate the resulting dipole moment by \int_0^R \int_0^{2\pi} \int_0^{\pi} r^3 sin(\theta) cos(\theta) 3 \epsilon_0 E_0 d\phi d\theta dr
but in this case the integral over \theta is zero and therefore this whole term will be zero which is somewhat strange, since there should be a dipole moment. So what am I doing wrong?
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