ELECTRIC FIELD PLOTTING

ELECTRIC FIELD PLOTTING

Abstract

The main aim of conducting the lab was to identify the electric fields of water bath system. The values obtained in the experiment were recorded. Some of these data include the strength and direction of the electric fields in a water bath. The results and analysis of data revealed that the electrical potentials remained the same in the second part of the experiment concerning equipotential lines. The equipotential lines minimized the errors. The results showed the strength of each metal bar in the water bath system. The results which were obtained from the experiment ranged from 1.00v to 6.69v. By application of Coulomb’s law, it was determined that slope under investigation was 50.32V/m. The lab demonstrated the relationship that existed between electric potential and electric fields. Moreover, we learned how to quantify the fields by applying the electric voltage potential readings.

Introduction

In this physics conducting lab, we emphasized on investigating the relationship that exists between the electric field and electric potential. Moreover, the electric field (E) defines a measure of the force that the field near an electrically charged particle would exert on another electrically charged particle. On the other hand, the electric potential (V) highlights the quantity of probable energy of a particle as a result of the specified electric field. The general relationship that is present between E and V is the slope.

Method

To start this experiment, we initially placed two metal bars in the glass container that had a shallow water level. Beneath the glass, a sheet of graph paper was placed. Nevertheless, the paper was used to line up the metal bars so that they become parallel to one another and note measurements. In addition, we used a function generator to effect both positive and negative charges to every bars so as to identify the one that was on the ground. An electric field was created by connecting metal bars to a power supply providing AC. The next step involved the use of a digital multimeter (DMM). The digital multimeter was used to plug in a probe. DMM was employed to measure the RMS voltage drop that existed between selected fixed location and a series of varying locations in the water bath. The measurements obtained were recorded according to the guidelines of the TA.

In the lab experiment, we quantified the electric voltage at numerous intervals on a conducting piece of paper. Additionally, we strived to identify equipotential lines and approximate the strength of the electrical fields. In the event of approximating the latter, a probe was used to quantify it by using a Direct Current (DC) voltage source. Nonetheless, upon the values are acquired, then the graph can be created to evaluate the slope. The slope defines the electric field potential as a function of distance from the positive electrode. Advancing with the experiment, a copper ring was included to the middle of the negative and positive electrodes. With the inclusion of the copper ring, the electric field altered to a new pattern which was demonstrated and recorded on a piece of paper. The electric field was quantified using a probe and thoroughly drawing out the equipotential lines in the whole system.

The second part involved introducing the coaxial rings that were positioned into the middle of the water bath. At this point, another water bath was set up according to the guidelines of the TA. The large ring and the small ring were charged differently in such a way that the large ring was charged positively, while the small ring was charged negatively. Electric fields were measured at an interval of 2cm along the axis. The data obtained were then recorded into graphed. To determine the direction of the vectors of the electric field E a two-point probe was used.

The lab experiment involved setting up a power supply of 10 Volts. A paper with two parallel lines was used. A single probe was set up to find a potential between the lines. Five equal potential lines were plotted, and five equal readings outside the parallel lines were recorded in the experiment. The values of electric voltage, V, against the electric field, E, were plotted to obtain the graph. Also, it was possible to get the experimental value E. The other probe was hooked up, and measurements in four locations were obtained inside the electric field. Then, some measurements were garnered outside the electric field, and the direction of the fields was noted. A two-dot electrode paper was put on the table, and four equipotential lines were made on the paper. The magnitude and the movements of the electric field were recorded. The last step was to calculate the values of electric field potential from the data that had been obtained before.

Results

The results of the investigation are shown in the tables and figures below. Table 1 highlights the measurements taken for the electric field potential and electric voltage.

Y-Axis in (Cm)

Electric Potential

(V)

Units

V/m

4

6.68

6

5.72

8

4.75

10

3.72

12.

2.72

14

1.72

16

1.00

Total voltage over a given distance

59.15

Voltage between two points

46.59

The value obtained from the double probe

40.96

Y-Axis in (Cm)

3

4.015

6

5.65

5

5.22

7

6.01

Table 1.The measurements taken for the electric field potential and electric voltage

The outcome from the experiment were as follows.

Equations of use are:

V(r)=2kλln (r) & E =(2kλ/r) r

Slope of V vs ln(r) is m = 2.34

With equationV(r)=2kλln (r). Reorganize to get λ so λ=V(r)/ln(r) * 1/2k

so λ = m*1/2k. λ = 1.3*10-10

Δλ = ((λ/m)*(Δm)2((1/2k)*(1.04)2 = 5.75*10-11 . So λ = 1.3*10-10 ± 5.80*10-11 charge per unit length.

Gradient E vs 1/r is m = 1.92

With equation E =(2kλ/r) r and considering that r = cos90 = 1. Rearrange the equation so that λ=Er/2k = m *1/2k So λ = 1.06*10-10

Δλ = ((λ/m)*(Δm)2((1/2k)*(.4986)2 = 2.80*10-11 So λ = 1.060*10-10 ± 2.80*10-11.

Figure 1. A diagram of the water bath

Figure 2. A diagram of the electrodes inside the water bath

Figure 3. A graph of the voltage (V) vs. distance

Figure 4. A graph of velocity vs.distance

Therefore, these figures can be tabulated as follows:

λV/ln(r)

1.29*10-10 ± 5.75*10-11

λE/(1/r)

1.064*10-10 ± 2.77*10-11

Analysis

The main objective of conducting this experiment was to identify and evaluate the patterns in an electric field and make a comparison with the anticipated behavior given by the Coulomb’s and Gauss’s laws (Kuffel et al. 2008, p.414). In this lab, it was also possible to examine the relationship that usually exists between the voltage and distance of the two electrodes. The voltage decreased in a linear manner with distance and the gradient represented by the electric field whose value was 50.3V/m. It was necessary to maintain this value at a constant figure. Also, the bars were large, and this made it possible to approximate them using the parallel lines and by the Law of Coulomb. The electric field was identified to be a constant at any location between the plates. The values of the electric field potential that were used in plotting the graph were similar to other electric field values attained from other methods. For instance, there was a large range of 40.9v/m that had been recorded from the double probe. A voltage of 59.16V was recorded in the whole experiment setup from the total potential difference. The value of the slope ranged between these figures. It was observed that there was a vast skewness that existed over a large distance as a result of electric voltage that is being measured over small intervals in the total distance.

In Part1b, the field lines illustrate how a conductor that is located in an electric field can influence electric potential and the electric field. The field lines are usually bent around the outer part of the conducting cylinder. A two-point probe was also used to measure the voltage at different points alongside a single-point probe. The electric field is usually a vector and is not a scalar, and this was the reason why a two-point probe was used to measure the velocity (Kuffel et al. 2008, p.490).

The vector of the electric field was determined by using a two-point probe by rotating it up to the time when the potential difference had reached an optimum level. The difference that was obtained in the potentials was later divided by the distance between the electrodes, and this was the factor for the magnitude and direction of the electric field. One electrode was sufficient to gauge the electric potential values of the field which is a scalar value. The electric field vector was perpendicular to the surrounding equipotential lines. It was possible to identify the notion that electric fields exist in a radial manner from a field whose center is positively charged. From this experiment, the voltage inside the ring was identified to be 0. This illustrated the concept of Gauss’s law. The outer part of the cylinder acted as a Gaussian surface. The charge was zero because no electrical charge existed within the Gaussian surface on all points on the outer part of the cylinder. There was a drastic change of the charge outside the sphere later on.

The second phase of the experiment involved the use of two cylinders which had a different radius. For instance, the inner cylinder was attached to the ground, while the outer cylinder connected to a high voltage wire. It was quite clear to identify that the equipotential lines were in the shape of the cylinders. This demonstrated the concept of Gauss and Coulomb laws. According to the law of Coulomb, the electric field is inversely proportional to the square of the radius. Therefore, the electric potential is always equivalent to points which have equal distance from the central point of the two concentric cylinders. On the other hand, Gauss’s law illustrates that flux and therefore the electric field always depend on the level of charge that the Gaussian surface has (Begamudre 2009, p.312).The points that are along a Gaussian surface usually have the same electric potential and magnitude in a certain electric field.

After carrying out the lab, the data and the respective graphs revealed that the experimental value E for electric field had a correlation with the theoretical values that had been provided. The various issues about the concepts of electric fields and the equipotential lines were explained. Interestingly, the potentials for the electric field were able to follow the equipotential lines as was anticipated.

There is a clear relationship that usually exists between voltage vs. In(r) and E vs. I/r. The relationships are suitable. Voltage can also be expressed as an integral value of the electric field over distance. Since the electric field is directly proportional to I/r when integrated on r, it is possible to calculate back In(r). There is a correlation in this relationship of the model that is explained theoretically in the procedures of the lab.

Λ V/ ln (r) = 1.3*10-10 ± 5.8*10-11

λ E/(1/r) = 1.059*10-10 ± 2.8*10-11

The values of λ were always consistent with the different calculations, despite the fact they were not consistent within the provisional errors of the experiment. The differences are brought about by the shifting of the rings specifically the smaller ones in water during the activity. The hand held the smaller rings in the water, and this could have influenced the discrepancy. There is a higher chance that during the experiment the one hand shifted in a different direction and resulted in some differences in the distance measurements or the computation of the distance. The reason for such errors is the poor contact between the conductive paper and the probe. Moreover, it can occur if the paper was pressed too hard on the probe. The error could also have been caused by one lab member who could have touched the conductive paper unintentionally. The sweat on a person’s hand could also be one of the contributing factors to this error. This would have an impact on the values of the voltage that were obtained through calculations (Begamudre2009, p.211).

The main aim and objectives of the experiment were achieved. Evidently, the relationship that existed between the electric field and electric voltage was established. The concepts of the laws of Coulomb and Gauss were illustrated in the lab. Consequently, from the values of V and E, the charge was equivalent to the distance of the electric field that was calculated using other different ways. The integral association of the charge and the respective electric field was illustrated by the comparison which was made in the two linear graphs. This information can be applied effectively in the physics by using potential differences inside the capacitors. The key reason for the equipotential lines was to determine the voltage distribution on the electrodes of the capacitor

Conclusion

This lab confirms that the electric potential between the plates is equal. The experiment also demonstrates that the electric field is perpendicular to all the equal potential lines of the electric field. Moreover, the electric field between the plates is also shown to be equal. The outside points of the cylinders which have an electric field have low magnitude and show different directions from the ones provided. This was demonstrated by the few errors that were found in the experiment. As explicated, the main objective of the lab was to identify the electric fields of water bath system.

In this lab, we demonstrated that the equipotential points offer a smooth curve of equipotential line. By applying these equipotential lines, we were able to reach the electric field lines. Moreover, in this study, the directions of electric field lines are gauged by having the awareness that the electric field lines elongate outwards from a positive to a negative charge. Due to some systematic errors, we found it difficult to assess the precise paths of equipotential and electric field lines. Human mistakes and making the study in a limited time interval address the systematic errors present in the experiment. I believe that more accurate measurements are necessary to quantify the equipotential points.

References

Begamudre, R. D. (2009). Electro-mechanical conversion with dynamics of machines New Delhi, New Age International

Gastineau, J. E., Appel, K., Baaken, C., Sorensen, R., Vernier, D., & Anderson, J. A. (2015) Physics with Vernier: physics experiments using Vernier sensors.

Kuffel, E., Zaengl W S, & Kuffel, J (2008) High voltage engineering: fundamentals Oxford, Butterworth-Heinemann/Newnes. Available at: <http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=210488>.

Melissinos, A. C. (2009). Experiments in modern physics Elsevier Science Pub

United States (2011) A directory of computer software applications–electrical and electronics engineering, 1970-Sept 1978 Springfield, Va, NTIS.

United States (2010) Energy research abstracts. [Oak Ridge, Tenn.], Technical Information Center, U.S. Dept. of Power.

United States (2011) Directory of computer software applications: electrical and electronics engineering. [Springfield, Va.], U.S. Dept. of Commerce, National Technical Information Service.

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