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Unformatted text preview: HW3 Phys5405 f02 due 9/17/02
1) An inﬁnitely long right cylindrical region of radius R has uniform volume charge density
ρ0 . It is surrounded by an uncharged coaxial right cylindrical conducting shell of inner radius
R’ (R’ > R) and outer radius R”. Find the E for a) ρ > R”, b) R < ρ < R’, c) ρ < R. Find
2) There are 3 parallel conducting plates of very large area A and thickness T. The top
plate has a total charge QT , the middle plate has a charge QM , and the bottom plate has
a charge QB . The vacuum distance between top and middle plates is d, while that between
middle and bottom plates is d’. You want to ﬁnd E above the top plate, below the bottom
plate, and in the regions of d and d’ far from the edges of the plates (assume you can neglect
edge eﬀects). Find the surface charge density on each surface of each plate. Also ﬁnd the
potential diﬀerence between top and bottom plate.
3) Show that the Schrodinger Equation, − 2m 2 Ψ = ih ∂ Ψ , is invariant under the Galillean
¯ ∂t transform, provided the wave function in the O’ frame is renormalized by a phase, Ψ = Ψeiα ,
where α = − mv (z − vt/2) and z is the direction of relative motion between O and O’. That
is, show that − 2m 2 Ψ = ih ∂ Ψ .
¯ ∂t 1 ...
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