# University of Maryland Computer Tutorials in Physics: Electric Forces

## I. Introduction

When we developed the laws of classical mechanics we learned that to determine what forces acted on an object we had to look for forces of two types: touching (contact forces) and non-touching (action-at-a- distance forces). Our main example of a non-touching force was gravity. The earth exerts a force on an object, pulling it towards it, even when the object does not touch the earth.

A second non-touching force is the electric force. Electric forces act only between objects that are charged while gravity acts between all masses. Another important practical difference between electrical and gravitational forces is that gravity is much weaker than electricity. It takes an extremely large object (the earth) to produce a noticeable gravitational force. This means that the distance scale over which the gravity force we are familiar with changes is on the order of the size of the earth.

Even very small objects can produce enough electric force to lift another small object, thereby overcoming the gravitational effect of the entire earth! As a result, electric forces change on a distance scale the size of small objects -- a scale we can readily observe.

In this tutorial, you will "become a test charge" and probe the forces you feel from a variety of fixed "source" charges.

## II. Familiarizing Yourself with the Program

Start the program EMFIELD. When the blue information screen appears, press enter to run the program.

To control this program, you will use the mouse to choose items from the menu bar at the top of the white screen. Click on Sources on the menubar, and choose the item 3D point charges from the pop-down menu that appears.

### A. Forces from a single charge

A set of numbered white and red circles now appear along the bottom of your screen. These represent point charges. Drag the positive point charge (filled in red circle) with number 1 into the center of your screen.

Now you will turn yourself into a test charge carrying an electric force meter. Starting from one side of the screen, hold the mouse button down (don't release it!) and slide around on the screen. The cursor becomes your "electric force meter". It displays the force you feel at any instant of time. When you are finished exploring the force, slide the cursor off the bottom of the display area before releasing the mouse button.

1. What happens to the (direction and magnitude) of the electric force vector as you approach the point charge?

Now grab the charge with the mouse and drag it off the bottom of the screen. Pick up the negative point charge (open circle) labeled -1 and place it in the center of your screen. Use your force meter to explore the forces you would feel from this charge. Again, do not release the mouse button until you have slid it off of the display area and are finished exploring.

2. What happens to the (direction and magnitude) of the electric force vector as you approach the point charge.

3. What is the difference between this case and the previous one?

B. Forces from many charges

Now place a variety of charges, positive and negative, on your screen. Make sure you have at least 4 charges present. Sketch their placement in the region at the top of the next page.

1. Explore the forces your test charge will feel in this region from the charges you have put down. Slide around in the entire region. Describe what you find in words.

When we are trying to compare the forces that our test charge would feel at different points in space, we have to move from one point to another. It is rather difficult to remember what all the forces looked like. Fortunately, the program has a device that can help us remember what we found. If you release the mouse button when the cursor is at some point, it will drop the force vector at that point and leave it there for future reference.

2. Now try the following. Go around your diagram and "drop" the forces your probe has observed at many points on the screen. Sketch the result you obtain in the box in the left below. You don't have to draw all the arrows you have dropped, just a few that show the main characteristics of the forces you have found.

3. Now grab one of the charges in your picture and drag it down below the bottom margin of the display area. It should disappear. Do your force vectors change? Some of them? All of them? Sketch the new force vectors in the box above on the right.

• To remove all the force vectors from your display without affecting the charges, choose Display/CleanUpScreen from the menu.
• To remove all the charges from your displaychoose Sources/3DpointCharges from the menu.
• (This will also remove the force vectors.)

The force vectors will readjust to include the effects of the new charges.

## III. Exploring the force from one charge

In this section we will explore the force from a single charge semi-quantitatively. For this you will need a centimeter ruler in order to measure distances and the sizes of the field arrows. A small plastic ruler about 15 cm long is preferable. If you don't have one, tear off the bottom of the last page of this tutorial and use the ruler there.

To help you be precise in your measurements, menu, choose Display/ShowGrid from the menu. Now go back to the menu and choose Display/ConstrainToGrid. This will constrain where the charges may go. You will still be able to probe the force your test charge will feel at any point (even between grid points).

Place a +5 charge somewhere near the center of your screen.

1. "Drop" electric force vectors at points one grid point, two grid points, and four grid points away from the charge at the x-marks in the figure at the right. Measure the length of the three force arrows.

Distance from charge (in grid units) Length of force arrow (in cm)
1
2
4
2. Does the force produced by the program follow a 1/r**2 law to within the accuracy of your measurement? 3. Clear the screen of force arrows by choosing Display/CleanUpScreen from the menu. Now measure the forces along a single radial line as shown by the x-marks in the figure at the left. How is this different from what you saw above? 4. Does the fact that the long force arrow overlaps the shorter ones have any meaning? Explain. 5. What do you think would happen if you instead had used a point charge of equal negative value? How would the direction and magnitude of the vectors in the above steps change? What if you used a positive charge of a different magnitude?

6. Do it. Does it do what you expected?

## IV. Exploring the force from two charges

### A. The dipole

With a clean screen place a charge of +3 and -3 at grid points near the center of the screen so they are two grid points apart (that is, they are on grid points and there is one grid point between them).

1. Explore the forces produced by these two charges by sliding around with the mouse button down. Describe in your own words what the forces you feel are like in different places.

2. Drop lots of arrows around the charges. Describe the pattern these arrows make.

3. Now clear the screen of arrows by choosing Display/CleanUpScreen from the menu. Drop force measurements on the grid points up and down the perpendicular bisector of the line joining the two charges as shown in the figure at the left. Sketch what the forces would look like if your test charge were at each of the marked points.

4. Why do they look like this?

5. Now without cleaning the screen, drag the negative charge out of the grid area. Describe what happens to the electric force vectors that you had already placed in the region.

6. Return the negative charge to its original place and remove the positive charge. Describe what happens to the electric force vectors.

7. Explore what happens as you approach the pair of charges from the outside. How does the force compare with what you would see from a single charge of +3?

8. The total charge of this system is zero, that is, it is a neutral system. As you approach the charge from the outside does the force remain very small? Why?

### B. Two positive charges

Replace your negative -3 charge by a positive +3 charge.

1. Investigate the forces your test charge feels as it runs up and down the grid along the line between the two charges as shown in the figure at the left. Sketch arrows on the figure indicating the magnitude and direction of the force.

2. Then investigate the forces the test charge would feel as it runs along the line joining the two charges as shown in the figure on the right below. Sketch arrows on the figure indicating the magnitude and direction of the force.

### C. Superposition

The results for the positive and negative charge differ rather significantly from those for the two positive charges. 1. Why does the result along the line bisecting the line joining the two charges differ? It might be useful to consider the forces produced by each charge separately. You can do this by dropping your field arrows and then removing one or the other of the charges.

2. How does the result differ along the line joining the two charges as you go away from the pair? Which case falls off faster? Why? Again, it might be useful to look at the force produced by each charge individually.

The M.U.P.P.E.T. Utilities is available from Physics Academic Software (phone 1-800-955-TASL for information or orders).

Edward F. Redish
Jack M. Wilson
Ian D. Johnston