# PHYSICS 220/230                   Lab 2: Electric Fields and Potentials

Objective:  To  investigate experimentally the concept of the electric field and to map (to represent graphically) some electric field lines for particular configurations of charge.

Background:  The electric field intensity is defined as the electrical force per unit of charge, or E = F/q. Theoretically, the electric field is determined by using a positive test charge q and determining the force acting on it at every point in space. The direction of the field is found by the laws of vectors and the rule that tells you whether the force is attractive or repulsive. Since a free charge moves in an electric field by the action of the electric force, then work (W = F * d) is done by the field in moving charges from one point to another (e.g., point a to point b ). To move a positive charge from "b" to "a" against the electric field would require work supplied by an external force. The ratio of the work done, W, to the charge, q, in moving the charge between two points in an electric field is called the potential difference, Vab, between the points: Vab = W/q. If a charge is moved along a path at right angles (i.e., perpendicular) to the field lines, there is no work done (W = 0) since there is no force component along the path. No work means no potential difference from point to point. Hence, the potential is constant along paths perpendicular to field lines. Such paths are called equipotentials. Thus, an electric field set up by charges may be "mapped" by determining the equipotential lines (equipotential surfaces in three dimensions) that exist in the region around the charges. Potential difference is easily read by a voltmeter, whereas the measurement of forces would present numerous experimental problems.

Exercise 1: Measuring Equipotentials

Schematic of apparatus

Introduction: The apparatus consists of a flat board on which is placed a sheet of carbonized conducting paper imprinted with a grid. The sheet has electrode configurations of conducting silver paint which provide an electric field when connected to a battery. The standard electrode configurations provided are two circular dots representing point charges of an electric dipole and two parallel linear electrodes representing a two-dimensional cross section of parallel plates. Place one conducting sheet on the board and connect the conductor wires from the battery terminals to the two electrodes. Make connections to the electrodes with thumbtacks to hold spade lugs in contact with the electrodes. The voltmeter measurements will be made using the Data Studio data acquisition program.

Please do not write on the carbonized conducting paper.

Investigation One - In this investigation you will use a voltage probe to sketch four equipotiential lines for the point charges of an electric dipole.  You will then sketch the electric field lines.

• Connect the battery to the electrodes representing point charges.
• Configure the computer to be used as a voltage meter.
• Open DataStudio and chose "Create Experiment"
• In the sensors window, double-click on "voltage sensor"
• In the displays window double-click on "digits" and choose three decimal places for your precision
• In the displays window double-click on "digits"
• Click on "start".  If the voltage display does not show three decimal places, click the arrow on the digits tab in the display window and change the precision with the pull-down menu.
• The voltage probe consists of two wires coming from the interface.
Why could you not take voltage measurements with only one of the wires from the interface?
Where is the "zero" or "reference" of potential?  In other words, on what part of the apparatus do you measure a potential difference of zero?  Explain.
• Connect the probe such that you can take voltage measurements from the electrode board.  You should be able to measure the voltage at various points on the board.
• Sketch the electrode configuration on the paper provided using the same coordinates as those of the painted electrodes on the grid of the carbonized paper. You will plot your data directly on this paper.
• The wire from the computer interface that has a free end is to be used as a probe to investigate how the potential changes in the region between the two electrodes. Since you will be graphing equipotential lines, first choose which equipotential line you will locate, for example, one might choose 0.3 volts.
• Place the tip of the probe against the conducting paper at various positions between the electrodes until you find a position such that the meter reads 0.3 volts. Each time it does, you have found another point on that equipotential. Plot the points' coordinates on the paper provided. About 6 to 8 points throughout the region will be sufficient for each equipotential value.
• Repeat the process for at least three other potential choices that are spread throughout the approximate 1.5 volt range, e.g., 0.6 volts, 0.9 volts, and 1.2 volts. The choices of the potential values may need to be different to suit your apparatus.
• Once you have finished plotting all your points on your paper, draw a smooth curve through each set of points that have the same potential and label each with its potential. You now have mapped the equipotentials around the electrodes.
• Since the electric field lines must be perpendicular to the equipotential lines, sketch, in a different color, dashed lines to represent the electric field.  Make sure to attach your plot into your notebook.

Investigation Two - Repeat investigation one for the configuration of parallel plates.  Make sure you disconnect the battery after finishing Investigation Two.

Exercise 2: Computer-Aided Field Mapping

Introduction: This Physlet enables you to construct a distribution of point charges and then simulate the resulting electric field and potential.  Experiment with the simulation and complete the exercises described below.

#### Check this box to draw field vectors:

Procedures and Discussion: Electric Dipole

Add one positive point charge and one negative point charge by clicking once on the buttons.  Select and drag the charges into positions that resemble the configuration you explored in the manual mapping exercise.  Now check the box that draws field vectors.  Note that the field vectors are another way of representing the electric field.  The arrow indicates the direction of the field and the color indicates the strength, where black is the strongest and blue is the weakest.

Compare the equipotential and electric field vectors in your simulation to those in your manual map.

Look carefully at the values of the equipotential lines. What is represented by the density of equipotential lines drawn by the applet?

Are the field vectors perpendicular to the equipotiential lines as you assumed for your manual map?  Explain why these lines should be perpendicular.  Print out a copy of your applet generated map for your lab manual.  Refer to the electrostatics lab if you have forgotten how to print an applet.

Obtain a test charge by clicking the "test" button.  When the electric field is sufficiently strong, the electric field vector at the position of the test charge is displayed.  In addition, when you select and drag the test charge, the electric potential is given at the bottom of the screen.  (Caution: the negative sign used in the potential readout is very small.)  Explore the field and potential with the test charge.  Where is the potential highest and lowest?  Where is it zero?  Is the electric field zero where the potential is zero?  Where is the electric field strongest and weakest?  Explain your answer to each question.

Procedures and Discussion: Parallel Plates

De-select the box that draws field lines.  Then add an additional positive and negative charge (note, new charges are placed in the same location each time so you must move old charges before you can see the new) and place them very close to the first charges so that the 2 positive charges are aligned parallel to the 2 negative charges.  How do the equipotential lines in the new arrangement differ from those in Exercise 1?  Now add several more closely-spaced charges to the positive and negative rows in order to simulate a pair of closely-spaced, oppositely-charged parallel plates.  Describe the equipotential lines in between the plates.  What happens near the edges of the plates?  Explain.

Add field vectors to the screen by checking the draw field vectors box.  Describe the electric field near the plates.

Use a test charge to explore the electric potential and the electric field in the vicinity of the plates.  What are the characteristics of these two physical quantities near the plates?

Print out a copy of your applet generated map for your lab manual.

 EField version 4.0 was written by Wolfgang Christian.