Electromagnetic Theory (comments to: moloney@nextwork.rose-hulman.edu)

EXCEL spreadsheets

The user may input the magnitude and coordinates of up to ten point charges and a separate test charge. The spreadsheet will calculate the force on the test charge, the field and potential at the position of the test charge, and the potential energy of the test charge. It also calculates the potential at the position of each of the ten point charges, and the potential energy of the charge configuration (minus the test charge). This spreadsheet can be used to check solutions to a wide spectrum of point charge problems typically assigned in introductory electricity and magnetism classes.

Test Charge | Coords of test charge | |||||||||||||

1.60E-19 | x(m) | y(m) | ||||||||||||

3 | 3 | |||||||||||||

Calculations for System | ||||||||||||||

Calculations for test charge | (does not include test charge) | |||||||||||||

Charge | Coords of other charges | Delta x | Delta y | Separation | Force components | Field Components | Work to position charge | Potential at test charge | Potential at Point do to other points | Work to position point in system | ||||

Point | Q(C) | x(m) | y(m) | (m) | (m) | (m) | Fx(N) | Fy(N) | Ex(N/C) | Ey(N/C) | U(J) | V(Volts) | V(Volts) | U(J) |

1 | 6.00E-06 | 0 | 0 | 3 | 3 | 4.2426407 | 3.39E-16 | 3.39E-16 | 2.12E+03 | 2.12E+03 | 2.04E-15 | 1.27E+04 | -1.08E+04 | -0.0648 |

2 | -3.00E-06 | 1.5 | 0 | 1.5 | 3 | 3.354102 | -1.72E-16 | -3.43E-16 | -1.07E+03 | -2.15E+03 | -1.29E-15 | -8.05E+03 | 4.63E+04 | -0.138857 |

3 | 4.00E-06 | 5 | 0 | -2 | 3 | 3.6055513 | -2.46E-16 | 3.69E-16 | -1.54E+03 | 2.30E+03 | 1.60E-15 | 9.98E+03 | 3.09E+03 | 0.0123429 |

4 | 0.00E+00 | 1 | 2 | 2 | 1 | 2.236068 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.91E+04 | 0 |

5 | 0.00E+00 | 3 | 4 | 0 | -1 | 1 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.25E+04 | 0 |

6 | 0.00E+00 | 4 | 4 | -1 | -1 | 1.4142136 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.26E+04 | 0 |

7 | 0.00E+00 | -0.02 | 0.07 | 3.02 | 2.93 | 4.2077666 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 7.31E+05 | 0 |

8 | 0.00E+00 | 0.08 | 0.07 | 2.92 | 2.93 | 4.1365807 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 4.96E+05 | 0 |

9 | 0.00E+00 | -0.02 | -0.03 | 3.02 | 3.03 | 4.2780019 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.49E+06 | 0 |

10 | 0.00E+00 | 0.08 | -0.03 | 2.92 | 3.03 | 4.2080043 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 6.20E+05 | 0 |

11 | 0.00E+00 | 9 | 9 | -6 | -6 | 8.4852814 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 5.59E+03 | 0 |

12 | 0.00E+00 | 4 | 1 | -1 | 2 | 2.236068 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 2.85E+04 | 0 |

Total Force | Total Field | Pot Eng | Potential | Sys Pot Eng | ||||||||||

Fx(N) | Fy(N) | Ex(N/C) | Ey(N/C) | U(J) | V(Volts) | U(J) | ||||||||

-7.81E-17 | 3.65E-16 | -4.88E+02 | 2.28E+03 | 2.35E-15 | 1.47E+04 | -0.095657 |

Download self-unzipping excel file coulomb.exe [Use 'Save File']

This spreadsheet solves Laplace's equation in cylindrical coordinates. A "pipe" is drawn on the previous sheet by entering in values for the potential of the pipe. In this case, the pipe has a constant potential of 100 V. It is assumed that the pipe is symmetric about the x-y plane, so in this case the pipe actually extends from z = -1.25 to z= 1.25. The pipe can easily be extended, or its potential changed by changing the values in the corresponding cells on the data sheet. Multiple pipes can be added if desired. The potential around the pipe can be recalculated by pressing "F9".

There are four different types of formulas on the data sheet. Normally the potential at a given cell is a function of the potentials of the 4 surrounding cells and the cell's distance from the z-axis. When r = 0 a special formula must be used or else the potential would be undefined. The third formula occurs at z = 0 where we take into account that the pipe is symmetric about the x-y plane. The fourth case only involves the cell at (r=0,z=0) which is a combination of the two previous cases.

If you wish to delete the existing pipe and add a new one, you must be careful that the correct formulas get put back in where the pipe was. To erase the existing pipe from this sheet, first highlight cells B11 to G11 and "copy" them. Next, put the cursor on cell B10 and "paste" the copied cells over the top of the existing pipe. A new pipe can now be entered by typing over the existing cells.

Download a self-unzipping file: pipepot.exe (corrected and generalized 7/6/98) [Use 'Save File']

This spreadsheet solves Laplace's equation in two dimensions. Unlike the "pipepot" problem, there is only one type of formula involved in the calculations: The value of a cell is the average of the cells around it. A potential is defined around the perimeter of the rectangle, and the resulting field can be recalculated by pressing "F9".

Values for the potential can also be put in the interior of the rectangle. To delete these potentials, copy a neighboring cell (not in the perimeter though) into the cell you wish to replace.

100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | |||

0 | 49.1 | 68.0 | 76.3 | 80.1 | 81.7 | 81.7 | 80.1 | 76.3 | 68.0 | 49.1 | 0 | |

0 | 28.6 | 46.6 | 56.9 | 62.5 | 65.0 | 65.0 | 62.6 | 56.9 | 46.6 | 28.6 | 0 | |

0 | 18.6 | 32.8 | 42.4 | 48.1 | 50.8 | 50.8 | 48.1 | 42.4 | 32.8 | 18.6 | 0 | |

0 | 12.9 | 23.7 | 31.6 | 36.7 | 39.2 | 39.2 | 36.7 | 31.7 | 23.7 | 12.9 | 0 | |

0 | 9.3 | 17.5 | 23.8 | 28.0 | 30.1 | 30.1 | 28.0 | 23.8 | 17.5 | 9.3 | 0 | |

0 | 6.9 | 13.1 | 18.0 | 21.4 | 23.1 | 23.1 | 21.4 | 18.0 | 13.1 | 6.9 | 0 | |

0 | 5.2 | 9.9 | 13.7 | 16.4 | 17.8 | 17.8 | 16.4 | 13.8 | 9.9 | 5.2 | 0 | |

0 | 4.0 | 7.6 | 10.6 | 12.7 | 13.8 | 13.9 | 12.8 | 10.7 | 7.7 | 4.0 | 0 | |

0 | 3.1 | 6.0 | 8.4 | 10.1 | 11.0 | 11.0 | 10.2 | 8.5 | 6.1 | 3.2 | 0 | |

0 | 2.5 | 4.9 | 6.8 | 8.2 | 9.0 | 9.1 | 8.4 | 7.0 | 5.1 | 2.6 | 0 | |

0 | 2.1 | 4.1 | 5.8 | 7.0 | 7.8 | 7.9 | 7.3 | 6.2 | 4.5 | 2.3 | 0 | |

0 | 1.9 | 3.7 | 5.2 | 6.4 | 7.1 | 7.3 | 6.9 | 5.8 | 4.3 | 2.2 | 0 | |

0 | 1.8 | 3.5 | 5.0 | 6.2 | 7.0 | 7.3 | 7.0 | 6.1 | 4.5 | 2.4 | 0 | |

0 | 1.7 | 3.4 | 5.0 | 6.4 | 7.4 | 8.0 | 7.9 | 6.9 | 5.2 | 2.8 | 0 | |

0 | 1.8 | 3.5 | 5.2 | 6.9 | 8.3 | 9.3 | 9.5 | 8.6 | 6.6 | 3.6 | 0 | |

0 | 1.8 | 3.6 | 5.6 | 7.6 | 9.6 | 11.3 | 12.2 | 11.5 | 9.0 | 4.9 | 0 | |

0 | 1.8 | 3.7 | 5.8 | 8.3 | 11.2 | 14.2 | 16.5 | 16.3 | 13.0 | 7.0 | 0 | |

0 | 1.6 | 3.4 | 5.7 | 8.7 | 12.7 | 17.9 | 23.2 | 24.1 | 19.6 | 10.3 | 0 | |

0 | 1.3 | 2.8 | 4.8 | 7.9 | 13.0 | 21.6 | 34.1 | 37.5 | 30.9 | 14.5 | 0 | |

0 | 0.7 | 1.6 | 2.9 | 5.2 | 9.9 | 21.4 | 54.1 | 60.9 | 52.1 | 16.6 | 0 | |

0 | 0 | 0 | 0 | 0 | 0 | 100 | 100 | 100 | 0 |

Download a self-unzipping file rectpot.exe [Use 'Save File']

ANALYSIS OF TWO INFINITE LINES OF POINT CHARGE

This spreadsheet allows the user to look at contour plots (both 2-D and 3-D) of the potential due to two parallel infinitely long lines of uniform charge distribution. The potential is plotted in a plane perpendicular to the charge lines. The user may specify both the charge density on the lines and the x,y coordinates of the lines. The graphs will automatically be updated with any changes in the data.

Note: Double-clicking on the tip of the axis of the graph allows the graph to be rotated for different views (must be done when the chart is highlighted).

Wire | X Coordinate | Y Coordinate | Charge Density | |||

#1 | -2.2 | 0 | 1 | |||

#2 | 2.2 | 0 | 1 |

Download a self-unzipping file: 2_lines.exe [Use 'Save File']