Making Mountains...out of potentials

Open Excel. Click in the block at the intersection of the row and column headings to select the entire worksheet.

By dragging on the edges of the row and column headings, adjust the worksheet so that the cells are small and square.

Click on cell A1 and enter the following formula. Keep a close eye on the parentheses. Your best bet is to select the text below, copy it, and then paste it into Excel

= charge1/SQRT((COLUMN(A1) - COLUMN(charge1))^2 + (ROW(A1) - ROW(charge1))^2)+ charge2/SQRT((COLUMN(A1) - COLUMN(charge2))^2 + (ROW(A1) - ROW(charge2))^2)

Now duplicate the formula in cell A1 to the rest of the cells in the first row, out to cell CZ1. The easiest way to do this is to first click on cell A1 to select it, then drag the small handle (in the lower right corner of the cell) to the right until you reach cell CZ1. The cursor changes into a thin "plus" sign when you are in the right position over the handle. Release the mouse and the formula will have been inserted into each cell.

While that row of cells (from A1 to CZ1) is selected, drag them down to cell CZ52. That will fill in a large grid with your formula.

Move to cell Z26 (It's hard to read the row numbers, but you can see where you are by reading the Name Box in the corner.) Replace the long formula with the single value of 3, to represent a +3 C charge. Click in the Name Box in the upper left corner of the spreadsheet and replace "Z26" with "charge1" without the quotes, of course. Notice that there is no space between the "e" and the "1". Now your formulas will refer to this particular cell.

While still on cell charge1 (formerly known as Z26) select Cells... from the Format menu and make the cell a bright red color. Move to cell AZ26, replace its formula with -3, to represent a negative 3 C charge. Then name the cell charge2, and make it blue.

When you are done, your screen should look like this:

Now comes the fun part...select from A1 to CZ52 by pressing the mouse down on CZ52 and dragging to cell A1, then releasing. Click on the Gallery icon in the toolbar so that you can make a graph. Then click Chart.

Select the first Surface graph and behold your handiwork! You've created a 3-D graph of the potential around a dipole. By clicking on the chart and moving the handles around, you can view the scene from different directions.

There are two pre-built spreadsheets for this. MakingMountains.xls (in the Files area of the website) shows the finished dipole. This is useful when talking about charges "rolling" down from high to low potential. It also helps you see why defining V = 0 at infinity makes sense. The area between the charges has V = 0, but E ≠ 0. MakingMountains2.xls shows the potential around four positive charges. The area between the charges has V ≠ 0, but E = 0.