*Note: This is from the Second Volume of Feynman's Lectures on Physics : Mainly Electromagnetism and Matter
And this is the excerpt from the book:
If the relative displacement of the two spheres is small, the net charge is equivalent to a surface charge (on a spherical surface), and the surface charge density will be proportional to the cosine of the polar angle.
i.e. $\sigma = \sigma_{0}cos\theta $
What is that theta?? What is polar angle?? This came out of nowhere.
Please derive this quantitatively if possible.