1. Introduction

• Desirable for this course
  • background (PHYS 305, PHYS 321, PHYS 326)
  • access to the system or a laptop!
  • familiarity with Linux
  • familiarity with Python
  
  
• "Physics" topics to be covered
  • electric fields and equipotentials
  • variational methods
  • distribution of charge in a conductor
  • Laplace's equation
  • fields due to moving charges
  • the wave equation
  • the diffusion equation
  • the time-dependent Schrodinger equation
  
  
• "Computation" topics to be covered
  • calculation of field lines and equipotential curves (contours)
  • random numbers
  • Monte-Carlo methods
  • solution of partial differential equations
    - relaxation methods: Jacobi and Gauss-Seidel
    - finite differencing in 1, 2, and 3 dimensions

• Electric field lines

• Here's a simple program to compute the electrical potential energy due to a collection of point charges.

• Exercise 1.1:  Compute the potential (phi) and the x-component of the electric field (Ex) at the point (y,y) due to the dipole defined by

  	nq = 2
  	q1 =  1.e-6,  x1 = -1,  y1 = 0
  	q2 = -1.e-6,  x2 =  1,  y2 = 0

  Write your program using arrays to store the charges and their positions, so that the number of charges can be easily modified. Plot phi and Ex as functions of y for -10 < y < 10 in steps of 0.1. Here's a simple script that illustrates some basic graphics.  [Solution]

• Some more practical discussion on how to compute electric field lines is presented here. The scripts mentioned in the document are field_line_loop.py and field_line_loop_2.py. They can be used as starting points for the following exercise. To draw the field line(s), arrange for your program to compute as lists the values of X and Y obtained after each step in the field-line calculation. Then use pyplot to plot the field lines as you go.

• Exercise 1.2:  Compute the field line through the point (2,1) due to the dipole defined in Exercise 1. Modify the step to limit the change in potential d(phi) to 10² volts, and stop the calculation when the magnitude of the potential exceeds 10⁶ volts. Also, follow the field in both directions to draw the entire field line.  [Solution]  [Interactive solution]