I am having difficulty with calculating field outside of a polarized sphere. It is a field of a dipole. What I get always stuck with is the calculation of the area charge density. I attach a picture. I need the distance of the speres surfaces to calculate the density from the volume charge density. Well I call the distance [tex]\Delta[/tex]R. And in every source I find that [tex]\Delta[/tex]R = cos[tex]\Theta[/tex] * l. But I have no ideat how to derive this. I tried some ways (the law of cosines for O O' A triangle) and I always got that this is just an approximation. However, none of the sources mention that it is an approximation. Can someone help?