L25. Electric Fields

L25. Electric Field and Potential Plotting

About your lab report: This is an in-class activity on mapping electric fields. The instructor or a work service student will check your work as you do it.

Goal: To investigate electric fields and potentials graphically

Prelab: Do the following before coming to your lab period.

Complete P17a and bring your solutions to class.
Read 20.1,2 of your textbook.
Download and install the EM Field software if you plan to use your laptop during the lab. (See Introduction below.)

Introduction

EM Field is an interactive program that lets you select charges, arrange them how you want, and then view the electric fields around them. To download EM Field to your computer, go to T:\Software\Physics\EM Field. Just double click on the Setup.exe icon and accept the defaults. EM Field is also available on the rolling cart computers in Physics Labs 1 and 2.

Getting used to the software. Go to Sources, then 3D point charges. You'll see a line of red circles with numbers in them at the bottom of the screen; these are the point charges, and the numbers are their charge magnitudes (with no units … a real shame). Drag one of the charges onto the screen. What do you think the field will be like? Click somewhere around the charge; notice that the bottom of the screen changes to show the length of a field vector of magnitude one; click on more places around the charge (near, far). Also notice that you can click and drag the charge to change its position, and click and drag around the charge to see the field vector at different points. If your screen gets messy, clear it by going to Display and then Clean up screen. Also, you can display a grid by going to Display … Show grid.

Each person will make their own drawings. Ask the instructor or a work service student to check your work at each of the check points indicated in red below.

A. Electric fields

Clear the screen, and go to Field and Potential … Field lines.
Place two opposite point charges 10 cm apart on the screen. Give one charge a magnitude of 2 or 3 times the other charge with the charge of larger magnitude being on the left. Check with the person working beside you so that each of you picks a different multiplier.
Click around in different areas to see the field as a whole (15-20 clicks around each charge should be enough). Be sure to get field lines completely around and between both charges. Leave your field on the screen or save it for use later in Part B.
Now turn a sheet of graph paper in landscape orientation. You are going to draw a diagram of the field lines on your paper. Use pencil so that you can correct your drawings as needed. Begin by marking the positions of the charges 10.0 cm apart. (The graph paper's major divisions are a centimeter.) Label the charges with signs and values and draw enough field lines to be representative of the field around and between the charges. Add to each field line an arrowhead showing the direction of the field.
Mentally divide your drawing into 4 quadrants with the x-axis being the line joining the charges and the y-axis being the perpendicular bisector of that line. See below. Select and label a point S which meets these requirements:

Point S is on one of your field lines, is in the second quadrant, and is about 2 cm above the line joining the charges and 3 cm to the left of the perpendicular bisector.

Use a ruler in drawing vectors to make sure that they're straight and that they are colinear with the line joining the source charge and test charge.

You'll be doing some of the following on your graph paper and some on a second sheet of paper. On your second sheet, letter your responses as lettered below.

You'll be drawing vectors to represent the fields E_1S and E_2S of the two charges individually. First, however, you'll need to determine how these compare to each other so that you can scale your vectors accordingly. On a second sheet of paper, determine an expression for the ratio of the magnitudes E_1S/E_2S in terms of the charges Q₁and Q₂ and the relevant distances R₁ and R₂. Then measure these distances on your diagram to the nearest 0.1 cm and calculate the numerical value of the ratio E_1S/E_2S. Again, do this work on your second page in order to avoid clutter.

Now that you know the ratio of the fields, decide on a scale factor for electric field such that the smaller of your field vectors (this should be E_2S) will be about a centimeter long. In order to do this, you may have to tape another sheet of paper onto one edge of your graph paper to extend the boundaries. Write your scale factor in the upper-right hand corner of your graph paper in the form Magnitude of E_2S = ___ cm. All of your E-field vectors from now on will be scaled to this factor.

Now you're ready to draw vectors. Extending from point S, construct each of the field vectors E_1S and E_2S to the correctly scaled lengths. Label the vectors.

Graphically add vectors E_1S and E₂_S to create the vector E_net,_S extending from point S. E_net,_S must have the correct length and angle relative to the other vectors. Therefore, do your construction as accurately as you can using the tip-to-tail method. A protractor may be helpful.
Compare your result with that of the person beside you if you haven't done so already.
Answer these questions on your second page: Does the E_net,_S vector point in the expected direction? How do you know what to expect?

Check Point 1. Before going on, ask the instructor or a work service student to check your work.

Now mark a point T which meets these requirements: Point T is on one of your field lines, is in the fourth quadrant, and is about 2 cm below the line joining the charges and 3 cm to the right of the perpendicular bisector.

You've already determined a scale factor in part g, so continue to use the same one. Calculate the ratios E_1T/E_2S and E_2T/E_2S on your second page. Write the results symbolically before evaluating them numerically. You'll need these results in order to scale E_1T and E_2T relative to E_2S.

Repeats parts h and i for the electric field vectors at point T.

Measure the lengths of E_net,S and E_net,T. Answer this on your second page: How does the magnitude of the net electric field at point S compare to that at point T? Why does this make sense? (Hopefully, it does.)

Check Point 2

B. Electric Potential

Use the same EM Field computer drawing as you used in Part A. Now you'll add equipotentials. An equipotential is a line for which all points are at the same electric potential. If you're familiar with contour lines on a topographic map, equipotentials are analogous. On a contour line, all points are at the same elevation. In the EM Field program, go to Field and Potential...Equipotentials. You'll draw 4 equipotential lines. Draw them by clicking on the line joining the charges at distances of 2, 4, 6, and 8 cm from the left charge.
Now add the 4 equipotential lines to the field on your graph paper. Note that the equipotentials are always perpendicular to field lines. That's because the electric field is the negative rate of change of potential with respect to displacement perpendicular to the equipotentials. Under the action of the field only, a positive charged particle would take a path in the direction of the electric field from higher to lower potential. Consider again the analogy with the contour lines on a map. An object free to move under gravitational forces would roll from a higher to a lower contour (elevation) along a path perpendicular to the contour lines.

Check Point 3. The instructor or work service student will mark two points A and B on your paper. You'll use these later. You'll need to read section 20-3 before completing the lab. You may complete the remaining parts out of class and submit them by the end of the week.

Now it's time for some calculations. Do these on your second page. First you'll need units. Assume that the units of charge are microcoulombs and the units of distances are centimeters. For each equipotential line, calculate the value of the potential by superimposing the potentials of the two point charges. See section 20-3.
Now calculate the amount of work in joules done by the field in moving an electron from point A to B.
Tell why the sign of your result in part d makes sense.