Problem Set 5

Due Wednesday, November 17, in lecture

Problem 1 [10 points] (from this Fall's prelim)
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 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.
Problem 2 [20 points]
A spherical dielectric shell, with inner radius a, outer radius b, and dielectric constant , 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 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 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.]

Last update: Tuesday, August 21, 2007 at 11:05:24 PM.