January 21, 2009
PHY 712 – Problem Set #3
Continue reading Chaper 1 & 2 in Jackson; homework is due Monday, Jan. 26, 2009.
1. Consider a one-dimensional charge distribution of the form:
ρ(x) =
0 for x≤ −a/2
ρ0x/a for −a/2≤x≤a/2
0 for x≥a/2,
where ρ0and aare constants.
(a) Solve the Poisson equation for the electrostatic potential Φ(x) with the
boundary conditions Φ(−a/2) = 0 and dΦ
dx (−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.