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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 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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Pre 2010

Uploaded on 08/17/2009

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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/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
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.

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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.

  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 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.