Physics, Art, and Programming Ben Hoffman

Having said all of those things about the program, Here are some of the beautiful results of all that hard work:

 

Here we have one of the types of drawings that is entirely possible to imagine and draw for humans but still looks very nice when drawn by the computer. Two opposite but equal charges are displayed here. As you can see there are no field lines coming in from the left. This is a direct result of the solution b) which is violation of Feynmans rules of drawing field lines. In all of these drawings, the clear holes are positive charges and the dark spots are negative charges.

We see here how easy it is to make a little change to the system and view the results. This is the same system from above, except that the positive charge value has been increased by a multiple of two. If you look carefully, you can see that the positive charge from this picture is a larger area than the positive charge in the last picture. This is because I intentionally left out the first vector drawing of the all of the positive charges so that they could be easily distinguished from negative charges. Since the electric field from this positive charges is larger than that of the last, the first, missing, vector is bigger.

As you may have guessed, this is two equal positive charges. It is a relatively simple system, nevertheless, its pretty cool!

 

Here are a few examples of tight clusters of charges that are nice and complicated.

This chunk of programming can be just as much of a learning tool as it is a fun time. Here we have a set of six charges that are lined up. All of them have an equal positive charge and they are all equally far away from their neighboring charges. This makes for a nice representation of homogenous charge distribution along a "long" strait line or in a plain (if you imagine that each hole represents many charges coming into and out of the screen). The charges towards the middle of the line are in a situation that simulates being in an infinite line of charge. As you can tell the lines near the middle are moving strait out and away from the line. This is a great example of how the 1/r^2 falloff is altered near a plate or line of charge.

These are great examples. You can see different field densities and formations in any one of these drawings.

Run Away!