Electric Field Mapping

• Theory:

  Electric Field and Equipotential Lines:
  The electric field is defined as the electric force a unit charge will experience at a given point in space. By moving the unit charge around, we can create a map of the electric field at various points. To represent that map, we draw electric field lines following the rules:

  • The lines always start from a positive charge and always end at a negative charge.
  • At any point, the density of the lines in the vicinity of that point is proportional to the electric field at that point.
  • At any point, the vector of the electric field is tangential to the electric field lines at that point.

  Electric Dipole:    Two charges with equal magnitude but opposite polarity are called "Electric Dipole".

  Relation between the Electric Field and the Electric Potential:
  If we know the electric potential at any point in space, we can determine the components of the electric field vector by followin the equations:
           
  If we have spherical symmetry, both the electric potential and the electric field depend only on the distance r from the charge and the relation between them can be written as:
           

• Preliminary Setup:
  • You need: Graphing Paper.
  • Go to Charges and Fields on-line simulation
    • Start the simulation by clicking on the "Run Now" button.
    • Select "Show E-Field", "Grid", "Show Numbers", and "Tape measure"


• Activity 1. Map the Equipotential lines of a single positive charge
  • Click and drag a "+1 nC" charge to the center of the viewing window.
  • Click and drag the volt probe, in the lower left corner of the applet, to a position of 4 V. Click on the plot button, so that you will see the 4-V equipotential line.
  • Repeat the previous step to plot the equipotential lines for 4 V, 6 V, 8 V, 10 V, 12 V, 14 V, 16 V, 18 V, and 20 V
  • Copy the diagram of E-Field lines and Equipotential lines on a graphing paper and attach it in your lab notebook.
• Activity 2. Map the Equipotential lines of a single negative charge.
  • Click and drag a "-1 nC" charge to the center of the viewing window.
  • Click and drag the volt probe, in the lower left corner of the applet, to a position of "-4 V". Click on the plot button, so that you will see the "-4 V" equipotential line.
  • Repeat the previous step to plot the equipotential lines for -4 V, -6 V, -8 V, -10 V, -12 V, -14 V, -16 V, -18 V, and -20 V
  • Copy the diagram of E-Field lines and Equipotential lines on a graphing paper and attach it in your lab notebook.
• Activity 3. Map the Equipotential lines of a dipole
  • Click and drag a "+1 nC" charge to the left on the viewing window.
  • Click and drag a "-1 nC" charge to the right on the viewing window.
  • In the lower left corner, type in 0 Volts and click on the "Plot" button.
  • Repeat the previous step to plot the equipotential lines for ± 2 Volts, ± 4 Volts, and ± 6 Volts.
  • Copy the diagram of E-Field lines and Equipotential lines on a graphing paper and attach it in your lab notebook.
• Activity 4. Map the Equipotential lines of two positive charges
  • Click and drag a "+1 nC" charge to the left on the viewing window.
  • Click and drag a "+1 nC" charge to the right on the viewing window.
  • In the lower left corner, type in 5 Volts and click on the "Plot" button.
  • Repeat the previous step to plot the equipotential lines for 6 Volt, 7 Volt, 8 Volt, 9 Volt, 10 Volt, 11 Volt, 12 Volt, 14 Volt, 16 Volt.
  • Copy the diagram of E-Field lines and Equipotential lines on a graphing paper and attach it in your lab notebook.
• Activity 5. Estimate the Electric Field between two equipotential lines
  • Click and drag a "+1 nC" charge to the center of the viewing window.
  • Plot the V₁ and V₂ equipotential lines.
  • Measure the distance from the charge to the V₁ line, r₁.
  • Measure the distance from the charge to the V₂ line, r₂.
  • Calculate the average distance r as:
    
             
  • Calculate the average el. field, E(r), as:
    
             
  • Data and results: Repeat the procedure above for all the values in the following table.
    
    

    V1 (V)	V2 (V)	r1 (m)	r2 (m)	r (m)	E (V/m)
    3 V	4 V
    4 V	5 V
    5 V	6 V
    6 V	7 V
    7 V	8 V

    
    
  • Results:
    • Using your data, plot E(r) vs. 1/r².
    • The graph should be a straight line. Calculate its slope__________
    • Compare the slope you calculated with what it should be. Write down the percent difference_______________
    • Bring your graphs to class.