Equipotentials 1.51

Thomas A. Moore  --  August 2007

This program displays equipotential curves on a plane for various charge distributions.

Creating charge distributions

To add a charge distribution to the screen, press the appropriate button along the lower left margin of the window. The item will be added at the center of the window. The program represents all objects as cross-sections in the plane of the window; for example the "plane" of charge looks like a bar but actually extends a distance above and below the screen that is equal to half the drawing width. Objects with an (E) in their names are oriented so that what you see is an end view; objects with (S) in their names are oriented so that what you see is a side view. Objects having significant length above and below the screen are drawn with an extra line somewhere to indicate the "depth dimension" of this object (compare, for example, the point charge with the line charge in end-view).

You can select an object by clicking on the place where its charge is displayed (an object just added is automatically selected). The selected object is drawn with a gray background; others have a white background. A selected object may be moved by dragging its charge indicator or by using the arrow keys (pressing the "option" key at the same time as the arrow key causes the object to move 10 pixels per keypress). The selected object's charge can be increased or decreased using the Up or Down buttons or by using the menu commands under the Action menu. The selected object can be deleted using the Delete button or the Delete key.

Drawing and interpreting the equipotential curves

When you have arranged the objects as you wish, you can draw the equipotentials by pressing the Draw button, the return key, or selecting Draw from the Action menu. The equipotential curves should appear in at most a few seconds (even though the calculation involves scanning over 250,000 pixels in search of equipotential lines). The difference between the lowest-level (gray) equipotential lines (in units of kq/d, where q is a generic unit of charge and d is the width of the drawing) is shown below the progress bar, and may be adjusted using the "greater than" or "less than" buttons. The light red lines are separated by 10 times this amount, and the dark red lines by 100 times this amount. The black line (if there is one) marks the φ = 0 equipotential, which is defined to be the value φ has at infinity. If you hold down the option (alt) key and move the mouse, the value of the potential at the cursor location will be displayed in the upper right-hand corner of the graph.

Visualizing the electric field

If you hold down the control key, and move the mouse over the equipotential graph, you will see an arrow that indicates the electric field magnitude and direction at the current location of the mouse. Holding down the shift key as well multiplies the length of the arrow by 10.

Concluding Comments

I have tried to make this program as transparent and as easy-to-use as possible. Please send any bug reports or feature requests to me at tmoore@pomona.edu. This program was written using REALBasic, a superb development environment for Macintosh, Windows, and Linux platforms. For more information, visit www.realbasic.com. This program is freeware, and may be freely distributed, used, and/or modified, subject to the terms of the GNU General Public License, version 2 or higher (http://www.opensource.org/licenses/gpl-license.php).