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Question: Consider 2 spheres of radius R and uniformly charged with density [itex]\rho[/itex], one positively, the other nagatively. The two spheres are particlely overlapping each other and their center are separated by a distance d (< 2R). Calculate the dipole moment of this system.
What I have done so far: The dipole moment is given by
[tex]\vec{p}=\rho \iiint \vec{r'} \ dV'[/tex]
I know the total dipole is the sum of the dipole of each sphere. I can calculate the dipole moment of one sphere using spherical coordinates but it becomes impossible to do so for the second sphere. Obviously rectangular coordinates is not an option.. I'm running out of ideas, what do you suggest I try?
What I have done so far: The dipole moment is given by
[tex]\vec{p}=\rho \iiint \vec{r'} \ dV'[/tex]
I know the total dipole is the sum of the dipole of each sphere. I can calculate the dipole moment of one sphere using spherical coordinates but it becomes impossible to do so for the second sphere. Obviously rectangular coordinates is not an option.. I'm running out of ideas, what do you suggest I try?