Problem Set 6

Due Wednesday, October 15, by 5pm

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Problem 1 [15 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 [15 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.]