Write all your work and intermediate steps to show how... Problem 1 (Similar to Problem 4.4) A point charge q...

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.