Introductory Laboratory Category

2002 AAPT Apparatus Competition Boise State University

Name: P. J. Ouseph

Address: Physics Department

University of Louisville

Louisville, KY 40292

Phone: 502 852 0918

Fax: 502 852 0742

E-mail: pjouse01@louisville.edu

Apparatus Title: Electric Fields and Equipotential Lines

Abstract (40-50 words)

The classic Cenco “Equipotential lines apparatus” is modified so that it can be connected to a computer through a Pasco 750 interface. A movable electrode attached to a potentiometer is used to measure the electric potential at any point on a carbon-coated paper. The voltage signal from the potentiometer gives information about the position of the moving electrode.

You must submit a complete description of the apparatus with this entry.

The description should be suitable for publication in a professional journal and be detailed enough that others can duplicate the apparatus. This description (made anonymous) will be available to the judges of the apparatus.

Electric Fields and Equipotential lines

P. J. Ouseph, Physics Department

University of Louisville, Louisville, KY 40292

Equipotential-lines experiment has a long history of more than seventy years and it is still being used in general physics laboratories with only minor changes in the equipment from the original one introduced by Central Scientific Company. The widely used equipotential-lines equipment was introduced by Central Scientific Company (CENCO) sometime between 1914 and 1932. An early description of it may be seen in the laboratory manual written by Marsh White in 1932.

Experiments in our general physics laboratories were recently modified to enable the students to collect and analyze data with the help of computers. Pasco 750 interface along with Pasco sensors such as voltage, current, charge, magnetic field, and temperature

sensors, are used to collect data. Science workshop software program is used to display data in digital and/or graphical form and to perform the required calculations. The interface output provides the necessary voltages (DC and AC) for most of the experiments performed in the laboratory.

Fig. 1. The copper electrodes are kept over conducting paper. In this picture the moving electrode, attached to the rheostat, is between the parallel electrodes. Same rheostat and moving electrode are also used to study electric field between the circular electrodes.

The equipotential lines equipment, compatible with the computer software and interface, we have designed is shown in Fig. 1. Two pairs of electrodes, a set of parallel electrodes and another set of circular electrodes, are fixed to an acrylic plate. Conducting papers are kept between the electrodes over the acrylic plate. The moving electrode, in contact with the conducting paper, is fixed to the slider of a rheostat with the help of an acrylic plug which assures there is no electrical contact between the moving electrode and the rheostat. The thin film resistor of the rheostat is 10 cm long. If a dc voltage is connected to the end terminals of the rheostat, the position of the slider can be obtained by determining the voltage at the middle terminal. The parallel electrodes are kept below two rulers. The rheostat is held in the white plastic “saddle” which can be moved along one of the rulers. The saddle also helps to keep the rheostat normal to the electrodes. The x-position of the moving electrode is obtained from the ruler and the y-position from the position sensor output which is the voltage reading at the middle terminal of the rheostat. The position sensor output and potential sensor output, which is the field potential at the moving electrode are connected to the interface inputs. For the experiment a dc voltage (four or five volts) is selected from the interface signal output and this voltage is applied to the two electrodes and to the outer terminals of the rheostat.

Before taking the data, the rheostat is positioned close to one end of the ruler and the movable electrode is moved to the electrode at zero potential. The movable electrode is slowly moved from one electrode to the other after starting the data collection by clicking on the data collection button on the computer screen. The potential read by the movable electrode versus y-position may be displayed graphically on the computer screen. Remember the y-position is calculated by the computer using the position sensor voltage. Data obtained in one such run are shown in Fig. 2. It is clear from Fig.2 that the electric potential is linearly increasing between the plates. The slope of the line and, therefore, the electric field is constant in this case. Similar data are then collected for different x-positions; the voltage versus y-distance lines, except when the rheostat is positioned close to the ends of the electrodes, are straight lines. From these curves x- and y- positions for different voltages, 0.25 volts apart, can be obtained and corresponding equipotential lines can be plotted.

Figure 3 shows the results obtained using the circular electrodes. Obviously the voltage-distance curve is not a straight line; the best fit to the data is a logarithmic curve. This result can be used to illustrate Gauss’s law. One can show from Gauss’s law that the potential should vary logarithmically as a function of distance when the field has cylindrical symmetry

Fig.2. Variation of electric potential between parallel plates.

Fig.3. Variation of electric potential between circular plates.