ELECTRIC FIELD VECTORS– 1302Lab1Prob1

You have been assigned to a team developing a new ink-jet printer. Your team is investigating the use of electric charge configurations to manipulate the ink particles. To begin design work, the company wants to use a computer program to simulate the electric field for arbitrary charge configurations. Your task is to evaluate such a program. To test the program, you use it to qualitatively predict the electric field of three different simple charge configurations (single positive charge, single negative charge, and dipole) to see if the simulations correspond to your expectations. Initially, you sketch the electric field vector for each of the three cases.

Instructions: Before lab, read the required reading from the textbook and the laboratory in its entirety. In your lab notebook, respond to the warm up questions and derive a specific prediction for the outcome of the lab. During lab, compare your warm up responses and prediction in your group. Then, work through the exploration, measurement, analysis, and conclusion sections in sequence, keeping a record of your findings in your lab notebook. It is often useful to use Excel to perform data analysis, rather than doing it by hand. At the end of lab, disseminate any electronic copies of your results to each member of your group.

Read: Tipler & Mosca Chapter 21 sections 21-1 – 21-5. It also might be a good idea to review Chapter 1 Section 1-6 & 1-7.

Equipment

You will use the computer application Electrostatics 3D. This program allows you to take position, potential and electric field data at any point near any given charge distributionin a 2D workspace.

If equipment is missing or broken, submit a problem report by sending an email to . Include the room number and brief description of the problem.

Warm up

1. Draw a positive point charge. Using the electric field formulation of Coulomb’s law, construct the electric field vector map for the positive point charge. (Remember that you can understand the electric field by considering the electric force on a positive “test charge” placed at that point.) Make sure to clearly define an x-y coordinate system. As you construct your map, pay careful attention to how the length and direction of the electric field vectors vary at different points in space according to Coulomb’s law for electric fields. Sketch a graph of the electric field as a function of x and also as a function of y.

2.Repeat question 1 for a negative point charge.

3. Repeat question 1 for a dipole charge configuration (one positive charge and one negative charge separated by a distance d.) Recall from the reading that multiple vectors at a single point are combined using the law of superposition (vectors add according to the tail-to-head vector sum rule). According to your coordinate system, which axis (x or y) is the parallel axis of symmetry? Which is the perpendicular?

Prediction

Determine the physics task from the problem statement, and then in one or a few sentences, equations, drawings, and or graphs, make a clear and concise prediction that solves the task.

Exploration and Measurement

In the folder Physics on the desktop, open Electrostatics 3D and click on the Point Charge button found on the far left side of the toolbar. A dialog box opens allowing you to enter the magnitude of the point charge, and whether it is positive or negative. To start out, you should de-select Draw Automatic E-lines from this charge. Once you select OK, you can place the point charge within the workspace by clicking the mouse button. You should take note of the position of the point charge, the x and y coordinates within the workspace are given at the bottom of the screen.

Click the Electric Field line button on the toolbar and move the cursor within the workspace to where you would like to evaluate a field vector. An electric field vector will appear with direction given by the arrowhead and the relative magnitude given by the length. Position and values for potential and field will be displayed on the bottom of the workspace. Clicking the mouse replaces the vector with an infinite field line, and moving the cursor will display new position, potential and field values for the new location. Repeat this procedure over consistent intervals (i.e. a grid) in the horizontal and vertical directions until you have created a reasonable table of data for the electric field.

Discuss in your group and note in your notebook:

  • What are the differences and similarities between the "field lines" and "field vectors" representations of the electric field?
  • Are they equally useful? Why or why not?

Repeat the above exercise for the electric field of a negatively charged point object. Save your result to a table. Discuss in your group and note in your notebook:

  • How does the vector field compare to that for the positive point charge?
  • What effect does increasing the change value have on the vector field map?

Finally, create a dipole by dragging two equalbutopposite point charges into the workspace. Make sure to take the position data for both point charges. Try a different spacing between the two charged objects in the dipole to see how that changes the electric field map. Try larger charges. If you are very far away from the dipole, how does the field compare to that due to a single charged point object? How about when you are very close to one of the charged objects in the dipole?

Make a table of the electric field caused by a dipole. It is especially important that you take your vector datamoving equal increments in the horizontal and vertical directions. Save your results to a table.

You should experiment with other electric field representations. Specifically, try to understand what role symmetry plays in the creation of electric fields.

Analysis

Consider yourdipole electric vector data.

  • Sketch the electric field as a function of position along the parallel axis of symmetry. Repeat for the perpendicular axis.How do these graphs compare with your prediction?
  • If you are very far away from the dipole, how does the field compare to that of a single point charge? How does it compare if you are very close to one of the point charges?
  • In general, where are the maxima and minima of the electric field? Does your answer depend on whether you are considering one or the other axes of symmetry? Why or why not?
  • Consider one of the electric field vectors in one of the diagrams you have created. If a positively charged object were placed at the tail end of that vector, what would be the direction of the force on it? What if it were a negatively charged object?How does the magnitude of the force compare to that of the force at a different point in space where the electric field vector is shorter or longer?

Conclusion

How does the computer-generated data compare with your corresponding predictions? What part of your prediction, if any, differed from the result? Why?

Suppose you placed a positively charged point object near the dipole at three different locations. If the object began at rest, how would it move? What about if it started with some given initial velocity?

Overall, was your prediction successful? Why or why not?