PHY 415: Electromagnetic Theory I
Prof. S. Teitel firstname.lastname@example.org ---- Fall 2007
Problem Set 4
Due Monday, November 12, in lecture
- Problem 1 [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 Eo. You may assume that each sphere is only influenced by the externally applied field and not by the other spheres.
- Problem 2 [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 Eo. 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 3 [20 points]
An infinitely long cylindrical shell of inner radius a and outer radius b, and of permeability µ, is placed in a uniform extermal magnetic flux density Bo 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.]