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A problem set from a university-level physics course, phy 712. It includes a one-dimensional charge distribution problem with four parts: (a) solving the poisson equation for the electrostatic potential, (b) finding the corresponding electrostatic field, (c) plotting the potential and field, and (d) discussing the results using gauss's law arguments. The homework is due on january 26, 2009.
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January 21, 2009
PHY 712 – Problem Set #
Continue reading Chaper 1 & 2 in Jackson; homework is due Monday, Jan. 26, 2009.
ρ(x) =
0 for x ≤ −a/ 2 ρ 0 x/a for −a/ 2 ≤ x ≤ a/ 2 0 for x ≥ a/ 2 , where ρ 0 and a are constants. (a) Solve the Poisson equation for the electrostatic potential Φ(x) with the boundary conditions Φ(−a/2) = 0 and d dxΦ (−a/2) = 0. (b) Find the corresponding electrostatic field E(x). (c) Plot Φ(x) and E(x). (d) Discuss your results in terms of elementary Gauss’s Law arguments.