hw02(1) - Princeton University-Physics 501 Problem Set 2...

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Princeton University—Physics 501 Problem Set 2 Due: October 4, 2011 1) A charge + q rests at the midpoint ( z = 0) between two infinite conducting planes, which are separated by a distance 2 a and held at zero potential. Find the potential everywhere in the space between the plates. 2) A point charge q is at the center of a very long grounded conducting cylinder of radius a . a) Find the potential inside and outside of the cylinder. b) Calculate and plot the ~ E field inside the cylinder—i.e., plot E z and E ρ as functions of ρ for z = a/ 2 and z = a/ 4. Hint: Treat the charge q as being spread over a small disc with surface charge density σ = 2 ( ρ ) where δ 2 ( ρ ) is the two-dimensional δ function defined as Z 0 δ 2 ( ρ )2 πρdρ = 1 . x = 0 ,y = 0 ,z = 0 and x = a,y = a,z = a . The walls z = 0 and z = a are held at a constant potential V . The other four sides are at zero potential.
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hw02(1) - Princeton University-Physics 501 Problem Set 2...

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