ELECTRIC FIELD. 2. If you have an equipotential surface that means that the potential difference is zero, along that surface. a. true b.

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1 ELECTRIC FIELD Pre-Lab Questions Page Name: Class: Roster Number: Instructor: Multiply Choice: Circle the correct answer 1. Electric field lines are drawn from a. positive charges to negative charges b. negative charges to positive charges c. the largest charge to the smallest charge d. the smallest charge to the largest charge 2. If you have an equipotential surface that means that the potential difference is zero, along that surface. a. true b. false 3. An equipotential surface has points in which the electric potential vary. a. true b. false 4. The relationship between the direction of the electric field lines and the equipotential surfaces is a. electric field lines are everywhere parallel to equipotential lines. b. electric field lines always intersect each other c. electric field lines are everywhere perpendicular to equipotential lines. d. electric field lines always make angles of 0 o and 90 o with equipotential lines. 1

2 ELECTRIC FIELDS OBJECTIVE: To determine the equipotential surfaces near charged objects and thus to map the electric fields in their vicinity. APPARATUS: Field Mapping Board and Probe AC Oscillator Oscilloscope Voltmeter Metric Ruler INTRODUCTION: An electric field at a point in space is specified by the force that would act on a charge q o, when placed at that point. E= F q o Equation (1) In principle, one would determine the magnitude and direction of E by measuring the force F exerted on a test charge q o. It is not feasible in general to measure the force directly, so we must use indirect means to evaluate E. The average electric field E, along the line between two points separated by a distance x may be calculated from the difference in electric potential (voltage) between the points. E ave = V 2 V 1 Equation (2) x The direction of E is in the direction from higher to lower potential. Equation 2 says that the average electric field E is equal to the space rate of change of the electric potential. It is possible to construct an AC electric model that simulates the static electric field and potential produced by static charges in two dimensions. One can infer the behavior of the static system from the AC model. If we can locate points in a plane that have a constant potential, V, these points may be connected by a line, called an equipotential line. Several lines of known potential may be drawn. Since electric fields must always be perpendicular to these equipotential lines, we may easily construct any number of these electric field lines. The distance between equipotential lines (and along the electric field lines) can be readily measured. Thus the magnitude and direction of E can then be found by means of equation 2. 2

3 METHOD: We have a conducting graphite plate with silvered electrodes to a field mapping board. An electric field, E, is produced in the plate by connecting the plate terminals, X and Y, to a source of AC potential. The metallic electrode at Y is connected to ground and thus has a potential of 0. The 8 series resistors divide the total potential difference between the electrodes, X and Y, into 8 equal potential differences. For example, if the total potential difference V = 4 Volts, then the drop of potential across each of the equal resistances is.5 Volts. The potentials at the points 1, 2, 3, etc., relative to the reference potential at V Y would be: V 1 = 3.5 V, V 2 = 3 V, V 3= 2.5 V,... V 7 =.5 V, V Y = 0 V Look at Figure 2. If we had 16 Volts (or a potential difference of 16) across the plates, we could find equipotential lines between the plates. For instance, the series of points labeled by the potential, 6V, in figure 2 make up an equipotential line. The horizontal lines are the electric field lines, which are always perpendicular to equipotential lines. The points of the same potential are obtained by means of the movable probe, which is connected, to the Cathode Ray Oscilloscope (CRO). This displays the potential difference, VAB, between the probe, and the movable contact, which is at the position 2 on the board. Let s say you have the movable contact in position 2. You will move the probe to positions where the AC signal on the oscilloscope is minimized (you ll see a relatively flat line). When you see one you ll put a dot on the paper. These dots connected will form the equipotential line. All of the points along this line are then at the same potential, V. The movable contact is then moved to position 3 and another series of points and resulting equipotential line is obtained. In this way the entire field between the electrodes is explored and mapped. 3

4 A.C. Voltmeter 1234 Frequency adjust Oscillator Amplitude adjust Oscilloscope 1 x X Y B Probe FIGURE 1 4V 6V X 1 8V 10V 12V 2V 14V 0V X 3 16V X 2 FIGURE 2( this is only an example) PROCEDURE: 1. Lift the Field Mapping board and attach the electrode configuration for two parallel plates. 2. Fasten a sheet of paper on the upper side of the board using the tape provided. 4

5 3. Using the appropriate template, (use the pegs on the plate) trace on the paper the electrode configuration that is on the underside of the board. Then remove the template. 4. Adjust the voltage output of the oscillator to 7 Volts as measured by the voltmeter. 5. The frequency of the oscillator should be adjusted to 1000 Hz. 6. Slide the probe onto the board so that the electrical contact on the bottom arm is below the board and the top arm, with the hole, is above the paper. 7. With the movable contact inserted into the board at position 1, move the probe around the board until the oscilloscope shows a minimum signal (null). (It doesn t have to be perfectly flat, just get close) 8. Using a pencil, place a dot on the paper at the position of the hole in the probe arm. 9. Move the probe to another "null" position and repeat step 8 all across the paper. The dots should be about a centimeter or so apart so that a smooth line may be drawn. 10. Move the contact at A to position 2 on the board and obtain the corresponding series of dots. 11. Continue this process by moving the contact, A, through each of the positions, 1 to Slide the probe off the board and remove the paper from the board. Draw a smooth line through each of the series of dots and, at the end of the line, label these equipotential lines with their potentials, 2V, 4V, etc. 13. Repeat steps 1 through 13 but this time attach the electrode configuration for a point charge and a plate.. CALCULATIONS: 1. Remembering that electric field lines must always be perpendicular to equipotential lines, draw a series of arrowed lines ( ) to represent the electric field. Draw about 10 or 12 lines across the entire paper. See figure 2 (this is not the actual configuration). 2. Using a metric ruler, measure the distances between equipotential lines, along E-field lines, at all of the points on the paper specified by your instructor. Enter these values on your data page. 5

6 NOTE: If your instructor has not specified which areas to study, then you should measure the distance between equipotential lines at the place where the lines are closest together and the place where they are farthest apart. 3 Indicate on each of your field mappings where the distance measurements, X, were taken. See figure 2 for an example. 4. Using equation 2, calculate the E-field strengths at the places specified. Enter the potentials in volts and the distances in meters. 5. Enter these E-field values in the calculations section. 6. Remember to do this for each the charge configurations. QUESTIONS: 1. Using a voltmeter, the equipotential lines around a charged particle were found. The following lines and their corresponding values were drawn. Equipotential line at 3 Volts Equipotential line at 7 Volts Charge a. Draw the electric field lines for this charge. b. Using a ruler, and equation 2, calculate the average value of the electric field between the equipotential lines. 2. Compare your graphs with those in your textbook for the configurations you mapped. How are they similar and how are they different, if at all? 3. In the middle of the space below, construct two point charges, one positive and one negative, separated by a distance of 2 cm. Draw several electric field lines connecting the two charge 6