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Calculating the Potential

Start up the PC and start WINDOWS (by entering win at the C: prompt). We will use the EXCEL spreadsheet program for calculating the potential using the relaxation method described above. We rely on the fact the potential at any interior point in a system will be equal to the average of its neighbours.

In a new workbook, define the region of cells that will correspond to your system. Choose a coordinate system, such as assuming that distance between adjacent cells is 2mm. You may wish to set the column widths to be fairly narrow (say 3 digits) so that more cells will be visible on the screen at a time.

To begin, set the value of each cell in the part of the spreadsheet corresponding to the system begin studied to zero. You can use the copy and paste functions to do this easily. We will leave the potential at the boundaries of our system at zero. Pick an interior cell. Set its value to be the average of its neighbours. For example, if you picked cell D3, you would set its value to =average(D2,E3,D4,C3). You can then copy this value to all of the interior cells in the spreadsheet. You may get a message that EXCEL can't resolve circular references, but that is okay.

We are now ready to change the potentials of certain cells to fixed values. This corresponds to putting fixed potentials on our electrodes in the Measurement part of the experiment. Start with a point at a fixed potential. Choose a point somewhere near the center of your system and change its value to a fixed value (say 100). At this point, you are ready to perform the relaxation calculation. From the TOOLS item on the Toolbar, select OPTIONS, then the Calculation window. There is a checkbox for Iteration, as well as a place to enter the maximum number of iterations and the size of the change to stop at for the calculated values. The default values are probably fine. Check the box, then watch the system perform the relaxation calculation.

You can use EXCEL to graph the resulting potential as a 3-D surface plot. To do this, select the region of the spreadsheet you wish to plot with the mouse, then select the Chart symbol. Select an empty region on your spreadsheet for the graph, then answer the questions for the Legend and axis labels etc.