Simulations of Electrical Interactions

Today’s lab will investigate the nature of electrical interactions between charged objects by means of simulation programs. There are two simulations and a number of options for each.

Electric Field Hockey is an educational game, where a charged puck must be steered around obstacles and into the net by using charges that are ‘stuck down’ to the surface (i.e. they are fixed). By adjusting the location of the sticky charges, you can generate the needed trajectory to make a goal.

EMField is a more traditional simulation that allows you to investigate the nature of the electric field vectors, electric field lines, electric potential, electric equipotentials, and Gauss’s law (plus a number of things dealing with magnetism). This program is differs from other simulations in that the charges can be dragged about the screen and the various quantities will automatically be recalculated for the new charge distribution.

Part One : Electric Field Hockey

Start the program ‘Electric Field Hockey’, and follow the onscreen instructions. Play the game for levels 1 and 3.  Sketch your solutions into your notebook.  Then solve game 5 and print the solution. Note: If you experience difficulty in solving the game, you may need to do the earlier games as well.   Answer the following questions using your solution to game 5.

• Look at the trajectory of the puck. At what points in the puck’s trajectory is the magnitude of its acceleration small or zero? How can you tell by looking at the trail left by the puck?  (hint: The dots are placed at equal time intervals.)

• At what points in the puck’s trajectory is its acceleration greatest? (Remember that acceleration is a vector.) How can you tell from looking at the trail left by the ball?

• Find a point on the trajectory where the net force on the puck was in a different direction than the puck’s velocity. Draw and label vectors showing the force on the puck and its velocity at this point. (Remember that the velocity is tangent to the trajectory, and that the direction of the acceleration is the same the direction of   the change in velocity over that time interval.)

• Turn on the force vectors (under the Display menu) and check your answers to the above questions.  Remember that acceleration is proportional to force.

Next add one more charge in the upper right corner of the screen. Is the trajectory altered? If so, print the screen, otherwise, move the charge around a little until the trajectory is altered, and then print the screen. Stay far away from your other charges. Finally, move the extra charge to the lower right corner, and repeat the previous steps.

• Since the Coulomb force falls off very rapidly with distance, one would expect that a far away charge would have negligible effect. However, in the previous exercise, you should have seen a large effect. Look at your printed screens and carefully compare the trajectories, especially along the first segment. Explain why the far-away charge had an appreciable effect.

Part Two: EMField

In EM field, you will be able to paste down the charge and produce a sketch of the force on a second object at a particular point in space. (Actually you will be looking at the Electric Force Field, usually called the Electric Field.) Open the Program EM field .  Select the Source menu and use 3D point charges. Drag a positive point charge onto the experimental area. In order to familiarize yourself with the program Click on the screen at points located on the perimeter of concentric circles. Sketch your results.

• What determines the size of the electric field?

• What determines the direction of the electric field?

• What test charge is assumed at the experimental point?

The next section is semi-quantitative in nature. Select the ‘Constrain to Grid’ option and the ‘Show Grid’ option. The charges will always be placed on one of the grid ‘dots’. However, you can still Click at any point that you desire. You can add more charge to a given location by dropping additional charge on top of the preexisting charge.

Dependence of the Electric Field on Charge

You will use the grid unit as a scale to measure lengths of representative force vectors to the nearest tenth of a grid square using the grid on the screen of the computer as a ruler. The first investigation is to see how does charge affect the size of the electric field at a particular point? To do this you will place a +2 charge on the screen. How long is the electric force vector at a distance of one grid unit away on the screen? Be sure to very carefully position the mouse before clicking, since the location is NOT constrained to the grid. Clean the screen and change to a charge of +4 by dropping a second +2 charge on the first. How long is the force vector one grid unit away on the screen? Clean the screen, and repeat with +8 units of charge. Record your data and write a conclusion.

Verify your conclusion by repeating the steps with +3, +6 and +9 charges. Measure one grid unit away. Record your results and state whether it affirms or contradicts your conclusion. Make a small GRAPH of the Electric Field versus the Charge.

• Is your line straight? If not make a second GRAPH of Electric Field versus (Charge)2.
• How does the magnitude of the electric field vector depend on the charge that is present? Explain?

Dependence of the Electric Field on Distance

Next, you will investigate how the distance from the charge affects the size of the electric field vector? To do this, use a +17 charge near the left edge of the screen. Carefully measure from the center of the charge to a point that is 1 grid unit, 2 grid units, ... and 6 grid units away from the charge. Click to generate the field vector and record your results. Make a GRAPH of Electric Field versus the Distance using Graphical Analysis. Note: once you have data for Electric Field (E) and Distance (x)  in Graphical Analysis, you can use that program to calculate related values such as 1/Distance, without having to use your calculator and type in new values.

• Is the line straight?
• If the graph is not linear, make a graph of Electric Field versus 1/Distance.
• If that graph is not straight, make a graph of Electric Field versus (1/Distance)2.
• Based upon your graphs, how does distance affect the size of the electric field vector? Explain.

Check your results by measuring the field one unit from a +10 charge.  Predict the force two grid units from the charge. Record your prediction and your measured result. Do you feel they agree well enough to support the model.

Now let’s look at dipoles.

• Place a +9 and -9 charge two grid units apart near the center of the screen.
• In your notebook, draw the two charges and roughly sketch a circle around them.
• Use your knowledge of addition of vectors, to predict the direction of the dipole field at the top, bottom and sides of the circle. This should be pretty easy.
• Now try to predict the direction of the field at points half way in between these around the circle. This is considerably more challenging.
• Now use the program to check your predictions.

• How do the results compare to your predictions.

• Explore the size of the electric field at various points around the dipole.

• What differences do you notice compared to a single charge.

• Comment of the pattern of the directions of the field. This may be easier if you change to directional arrows only. (Under Fields and Potentials menu) This eliminates the magnitude of the field information and makes all the arrows the same size.

The program will also draw those cute electric field pictures you have been seeing in your textbook. Clear the screen. Switch to Field Lines and click around to draw in some lines. Does it look as you expected? Now change one of the charges so you no longer have symmetry. What does this do to the pattern? Are there some parts of the pattern that don’t change much while other parts do? Make both charges the same sign. What does this do to the pattern? Does the field look as you would expect at large distances from the charges?