2. Plotting Field Lines and Equipotentials

• Ingredients for the field-line plotter:

  • a function to compute the potential phi(x,y)
  • a function to compute the electric field E(x,y)
  • a function to take a step of specified length in the local direction of the E-field
  • a function to choose (place limits on) the step
  • a function to set up the charge distribution
  • a function to draw the field line through a specified point, stopping the calculation on a negative charge or when the line is too far from the origin
  • a function to draw all the field lines originating near a positive charge
  • a main program to set parameters and oversee the calculation

• Demonstration 1

• Equipotentials may be handled somewhat similarly (now taking a step in the direction perpendicular to the local field), except that

  • the choice of initial conditions is different

  • we have a measure (dphi) of how far we are from the correct equipotential, so we can in principle apply a correction at the end of each step to force us back onto the correct track

  • the equipotentials from closed loops, so special care must be taken to make the loops actually close:
    • use a symmetric integrator
    • stop when "near" the initial point

• Demonstration 2

• Homework #1