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PHY 415: Electromagnetic Theory I
Prof. S. Teitel stte@pas.rochester.edu  Fall 2017
Problem Set 5
Due Tuesday, November 14, in lecture
 Problem 1 [20 points]
A spherical dielectric shell, with inner radius a, outer radius b, and dielectric constant ε, is placed in a uniform external electric field E_{o}. Find the electric field outside the shell (r>b), inside the shell (r<a), and in the dielectric (a<r<b). What is the field inside the shell in the limit that ε gets infinitely large?
 Problem 2 [20 points]
An infinitely long cylindrical shell of inner radius a and outer radius b, and of magnetic permeability µ, is placed in a uniform extermal magnetic flux density B_{o} which is directed at right angles to the axis of the cylinder. Find the magnetic flux density B outside the cylinder (r>b), inside the cylinder (r<a), and within the shell (a<r<b). [Hint: express the magnetic field H in terms of a scalar potential, and use separation of variables in cylindrical coordinates.]
 Problem 3 [10 points]
Consider a "dielectric" material formed by a regular cubic lattice of small conducting spheres. The radius of the spheres is R and the spacing between the spheres is d. Assume d>>R.
Find the linear dielectric constant ε for this material in the presence of an applied field E_{o}. You may assume that each sphere is only influenced by the externally applied field and not by the other spheres.

