Problem 1. (a) [30%] A hydrogen atom (with the Bohr radius of 5.3×10-11 m) is situated between two metal plates 3.0 mm apart, which are connected to opposite terminals of a 200 V battery. (The polarizability is given in Table 4.1.) What fraction of the atomic radius does the separation distance d amount to, roughly? Estimate the voltage you would need with this apparatus to ionize the atom. Problem 2. (a) [30%] A point charge Q = 10 μC is situated a distance r = 5 mm from a neutral hydrogen atom. (The polarizability is given in Table 4.1.) Find the force of attraction between them. [Hint: The point charge creates the field at the position of the neutral atom and, thus, polarizes it and induces a dipole moment. In turn, this induced dipole moment exerts a nonzero attractive force on the point charge. This is the force that you need to find.] Problem 3. A very long cylinder of radius R carries a polarization P(s) = k s² ŝ, where k is a constant and s is the vector from the center. (a) [20% points] Calculate the bound charges σb (on the surface) and pь (in the volume). (b) [20%] By making use of the Gauss's law, find the electric field inside and outside the cylinder.