Download PHY 3323 November 2, 2009 Exam #2 . . . correpta sub undis

PHY 3323
November 2, 2009
Exam #2
. . . correpta sub undis
Scuta virorum galleasque et corpora volvit . . .
Apparent rari natantes in gurgite vasto.
Virgil
Aeneid I, 100-1, 118
(1) A point charge q of mass m is released from rest at a distance d from an infinite
grounded conducting plane. How long will it take for the charge to hit the plane? (25
points)
(2) A thin insulating rod, running from z = −a to z = +a, carries the indicated line charge
densities λ(z). In each case find the leading term in the multipole expansion of the
potential.
a) λ(z) = k cos(πz/2a) where k is a constant. (10 points)
b) λ(z) = k sin(πz/a) where k is a constant. (10 points)
c) λ(z) = k cos(πz/a) where k is a constant. (10 points)
(3) A point charge q is imbedded at the center of a sphere of linear dielectric material with
susceptibility χe and radius R.
a) What is the electric displacement vector? (10 points)
b) What is the electric field vector? (10 points)
c) What is the Polarization vector? (10 points)
d) What is the bound charge density ρb and the bound surface charge density σb ?
(10 points)