Write all your work and intermediate steps to show how much you know and avoid unrelated writings. Problem 1 (Similar to Problem 4.4) A point charge q is situated a large distance r from a neutral atom of polarizability α. Find the force of attraction between them. Problem 2 (Similar to Problem 4.5) In Fig 4.6, p1 and p2 are (perfect) dipoles a distance r apart. What is the torque on p2 due to p1? Problem 3 (Similar to Problem 4.10) A sphere of Radius R carries a polarization P(r) = kr where k is a constant and r is the vector from the center. a) Calculate the bound charge σb and ρb b) Find the field inside and outside the sphere. Problem 5 (Similar to Problem 4.14) When you polarize a neutral dielectric, charge moves a bit, but the total remains zero. This fact should be reflected in the bound charges σb and ρb. Prove from equations 4.11 and 4.12 that the total bound charge vanishes. Problem 6 (Similar to Problem 4.15) A thick spherical shell (inner radius a, outer radius b) is made of dielectric material “frozen-in” polarization P(r) = ̂ where k is a constant and r is the distance from the center (Figure 4.18). (There is no free charge in the probem.) Find the electric field in all three regions ( r < a, a < r < b, r > b) by using displacement vector. Problem 8 (Similar to Problem 4.19) Suppose you have enough linear dielectric material, of dielectric constant εr, to half fill a parallel plate capacitor (Fig 4.25). By what fraction is the capacitance increased when you distribute the material as in Figure 4.25a? Problem 9 (Similar to Problem 4.20) A sphere of linear dielectric material has embedded in it a uniform free charge density ρ. Find the potential at the center of the sphere (relative to infinity), if its radius is R and its dielectric constant is εr. Problem 10 (Similar to Problem 4.21) A certain coaxial cable consists of a copper wire, radius a, surrounded by a concentric copper tube of inner radius c (Figure 4.26). The space between is partially filled (from b to c) with material of dielectric constant εr, as shown. Find the capacitance per unit length of this cable.