Unformatted text preview: HW 5 Phys5406 S06 due 3/2/06
1) A conducting, non-magnetic sphere, one described by = 0 , with radius a and uniform
surface charge density is spun with constant angular velocity the magnetic eld inside and outside the sphere. Why is Htan ! about a diameter. Find not continuous at r=a? 2) A uncharged sphere of radius a is an ohmic conductor with conductivity g and permitivity
. Suppose it is placed in a uniform electric eld E0. Now what is the electric eld inside and outside the sohere? What charge distribution is responsible for the eld? Where does
it come from?
3) JDJ 6.8
4) Let's revisit the problem of a dielectric sphere placed in a uniform electric eld, here E0 ez
(see JDJ section 4.4). If the sphere is homogeneous and isotropic, it is described by a single
permitivity . What if the sphere was described by Dx = x Ex ; Dy = y Ey ; Dz = z Ez . Here
the three s may be dierent. Obtain the equations given by the boundary conditions that
you have to solve to get a solution. There are too many coupled equations so don't try to
solve, however, show that when all three s are the same, there equations give the expected
result. 1 ...
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