PHY 339 Analytical Mechanics

MWF 9-9:50 AM OPL 103 http://www.wfu.edu/~natalie/f99phy339/

Instructor: Natalie Holzwarth Phone:758-5510Office:300 OPL e-mail:natalie@wfu.edu

Homework Assignments

Oct. 18, 1999

PHY 339 -- Problem Set PHY 339 - Problem Set # 1

Read Chapter 1 in Griffiths.

  1. Work Problem #1-48 in Griffiths.

Oct. 20, 1999

PHY 339 -- Problem Set PHY 339 - Problem Set # 2

Read Chapter 2 in Griffiths.

  1. Work Problem #2-12 in Griffiths.

Oct. 25, 1999

PHY 339 -- Problem Set PHY 339 - Problem Set # 3

Continue reading Chapter 2 in Griffiths.

  1. Work Problem #2-21 in Griffiths.
  2. Work Problem #2-31 in Griffiths.

Oct 27, 1999

PHY 339-- Problem Set PHY 339- Problem Set # 4

Complete reading of Chapter 2 of Griffiths.

  1. Consider a neutral hydrogen atom having a proton with charge density e0 d3(r) and an electron in its ground state having a density
    e0
    pa03
    		 e-2r/a0,
    where a0 is the bohr radius (0.529177249 Å). (Here we have denoted the elementary charge as e0 in order distinguish it from the natural number e = 2.7182818...) Show that the electrostatic potential associated with this atom is given by
    V(r) = e0
    4 pe0 r
    		 æ
    ç
    è     		1 + r
    a0
    		 ö
    ÷
    ø     		e-2r/a0,
    using the following two methods:

    1. V(r) = e0
      4 pe0
      		ó
      õ       		r(r¢)
      |r - r¢|
      		 d3r¢
    2. Ñ2 V(r) = - r(r)/e0.

File translated from TEX by TTH, version 2.20.
On 27 Oct 1999, 08:22.
Oct 28, 1999

PHY 339-- Problem Set PHY 339- Problem Set # 5

Start read Chapter 3 in Griffiths.



    1. Consider a one-dimensional charge distribution of the form:
      r(x) = ì
      ï
      í
      ï
      î
      0     
      for  
      x £ -a/2
      r0 x/a     
      for   
      -a/2 £ x £ a/2
      0       
      for   
      x ³ a/2,
      where r0 and a are constants.

      1. Solve the Poisson equation for the electrostatic potential F(x) with the boundary condition F(x ® -¥) = 0.
      2. Find the corresponding electrostatic field E(x).
      3. Plot F(x) and E(x).
      4. Discuss your results in terms of elementary Gauss's Law arguments

    File translated from TEX by     TTH, version 2.20.
    On 28 Oct 1999, 21:29.
    Nov. 1, 1999

    PHY 339 -- Problem Set PHY 339 - Problem Set # 6

    Continue reading Chapter 3 in Griffiths.

    1. Consider the "classic" image charge problem discussed in section 3.2.1 in Griffiths. In that problem, the potential due to a point charge a distance d from a grounded conducting sheet is determined for z>0. From the potential, the surface charge is calculated and the force and energy associated with the attractive interaction between the point charge and sheet is calculated. Consider the same problem for and UNGROUNDED sheet. Assume that the sheet has an area A and that d is small compared to the dimensions of the sheet.

    Nov. 3, 1999

    PHY 339 -- Problem Set PHY 339 - Problem Set # 7

    Continue reading Chapter 3 in Griffiths.

    1. Problem # 3.15 in Griffiths.

    Nov. 5, 1999

    PHY 339 -- Problem Set PHY 339 - Problem Set # 8

    Continue reading Chapter 3 in Griffiths.

    1. Problem # 3.18 in Griffiths.

    Nov. 8, 1999

    PHY 339 -- Problem Set PHY 339 - Problem Set # 9

    Complete reading Chapter 3 in Griffiths.

    1. Problem # 3.30a in Griffiths.

    Nov. 17, 1999

    PHY 339 -- Problem Set PHY 339 - Problem Set # 10

    Continue reading Chapter 4 in Griffiths.

    1. Consider example 4.7 on page 186 in Griffiths. Work through this example with the following modification. Denote the dielectric constant inside the sphere as e2. Suppose there is another dielectric medium outside the sphere denoted by e1. Find the fields inside and outside the sphere in terms of the constant applied field E0.

    Nov. 17, 1999

    PHY 339 -- Problem Set PHY 339 - Problem Set # 11

    Continue reading Chapter 4 in Griffiths.

    1. Problem 4.38 in Griffiths.

    Nov. 29, 1999

    PHY 339 -- Problem Set PHY 339 - Problem Set # 12

    Start reading Chapter 5 in Griffiths.

    1. Problem 5.24 in Griffiths.

    Dec. 1, 1999

    PHY 339 -- Problem Set PHY 339 - Problem Set # 13

    Continue reading Chapter 5 in Griffiths.

    1. Problem 5.29 in Griffiths.

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