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PHY 712 Prob Set #3: Solving Poisson Eq. for 1D Charge Dist. - Prof. Natalie Holzwarth, Assignments of Electromagnetism and Electromagnetic Fields Theory

A problem set for phy 712 students, focusing on solving the poisson equation for a one-dimensional charge distribution using given boundary conditions. Students are required to find the electrostatic potential φ(x) and the corresponding electrostatic field e(x), as well as plot both functions. The problem is discussed in terms of gauss's law arguments.

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Pre 2010

Uploaded on 08/18/2009

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January 25, 2008
PHY 712 Problem Set #3
1. Consider a one-dimensional charge distribution of the form:
ρ(x) =
0 for x a/2
ρ0x/a for a/2xa/2
0 for xa/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(a/2)/dx = 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.

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January 25, 2008

PHY 712 – Problem Set #

  1. Consider a one-dimensional charge distribution of the form:

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 dΦ(−a/2)/dx = 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.