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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)