A tiny scrap of paper is suspended motionless below a plastic pen that carries a net charge of Q. Focus on a single carbon atom in the scrap of paper. Suppose that the center of the outer electron cloud (with a charge of -4e) of this carbon atom shifts a distance s when the carbon atom is polarized by the pen. Required:
a. Use the momentum principle (Newton's 2nd Law) to derive a mathematical (algebraic) expression for s.
b. Using your result for s, derive an algebraic expression for the atom's polarizability, a.