Study of relationship between the potential and the position for two electrode configurations

Study of relationship between the potential and the position for two electrode configurations

Aracely Benitez ● Antonio Cid ● Fernanda Garrido

Mr. Andrés Concha

Section 2

Abstract

The objective of this paper is to compare the relation between distance or radius and the electric potential. First the distance and the electrical potential between two parallel lines will be compared. And later the electrical potential will be compared with the radius of two coaxial circles. From this the data it’s possible to conclude a directly proportional relationship between potential and distance or ln(radius).

Introduction

For this paper the objective is to study the behavior of electric field through the study of the equipotential lines. Also to determine experimentally the relationship between the potential and the position for two electrode configurations. To obtain that, the experiment consisted in measure the potential of a circuit.

First for the coaxial cylindrical electrodes two circles with two different radius were drawn with a conductive pen in a conductive paper and a metal pin was inserted in each circle. Two cables were connected to the pins, one connected to the generator and the other one to the voltmeter. The one connected to the voltmeter was moved to measure different potential in different distances from the pin in the shorter radius until it reached the bigger one.

Image 1: Coaxial cylindrical electrodes.

The second one for the surface electrodes two parallel lines drawn in the conductive paper with the conductive pen. The same process was repeated from one pin to the other. For both cases the data was written down in a comparative table and later graphed comparing the potential and the distance.

Image 2: Parallel electrodes.

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Image 3: Experimental setup.

Body

Like it was mentioned in the introduction two methods were used to obtain the relationship between the potential and the position for two electrode configurations.

Using the first and second method we acquire the following values:

For

Graph 1

As we can see from the graph there is a relationship between the volts values and distance. That relationship is directly proportional.

Graph 2

On the other hand for the coaxial cylindrical electrodes the relationship between electric potential and natural logarithm of the radius is also directly proportional. Comparing graph 1 with graph 2 it´s possible to notice that on having applied the natural logarithm to the radius a value is obtained by major accuracy. What can be verified by the mistake of the slope, since it has a very near value to 1 (0.9973).

Conclusion

Looking at the graphics it is easy to see that the relationship between the potential and the distance it is directly proportional. For the two circles the potential it is directly proportional to the ln(r) and for the parallel lines the potential is directly proportional to the distance, both cases in centimeter. Therefore there is verified that:

, for this case in two dimensions.

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