Lab 1: Electric Field Measurements

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1 My Name Lab Partner Name Phys 40 Lab Section Lab 1: Electric Field Measurements Objective: In this lab we measured the electric potential and electric field produced by applying a positive voltage to the center of a piece of carbon paper, while keeping one or all edges grounded. This was done for two different configurations, which emulate the types of problems one may see in their electrostatics homework. I feel that by doing these types of problems in the lab, it can help students improve their physical intuition about the course material. Procedure: This lab consists of two portions. I will first go over the procedure for the first part of the lab: Relation between equipotential curves and electric field vectors. I will then go over the procedures for the second part of the lab: Electric field and potential of a point charge. For the first part of the lab, we looked to measure the equipotential curves around a positive point charge that was positioned close to a grounded strip of conducting paint. A diagram of this setup and an equipotential curve can be seen in figure 1. To create this setup, we first took a piece of carbon paper which had a solid line painted across the bottom edge using metallic paint. A small dot of metallic paint was placed approximately 5 centimeters from the strip of paint along the bottom edge. The reason we used carbon paper was because it acts as a conducting plane. We used metallic paint because it creates a separate conducting surface, which can be kept at a constant potential. This is important because we need to make sure that the entire bottom edge of the carbon paper is grounded. The carbon paper was fastened to a cork board using non-conducting thumb tacks. We then screwed a metal hook onto the dot of metallic paint. Extra care was taken when screwing in the metallic hook; if the bottom was not completely flush with the paint, we would not get proper measurements. We attached the positive terminal of a voltage source to the hook, and the negative terminal to the strip of metallic paint along the edge. We then powered on the voltage source and set the voltage to 25V. To measure equipotential curves, we used a voltmeter which had the negative terminal attached to the grounded strip of paint, and a probe attached to the positive terminal. The probe was then used to find lines where we measured the same voltage. These spots were marked using a color pencil. However, it was difficult to accurately mark the exact spot we measured with the probe, which added a source of uncertainty to our equipotential curves. We then measured electric field lines at 4 different locations on each of the equipotential curves. To do this, we first attached another probe needle to the negative terminal of the voltmeter.

2 Figure 1 A diagram showing the layout used in the first portion of the lab. A positive point charge was created on a piece of carbon paper, and line of metallic paint was applied to one edge of the paper and grounded. Image taken from lab manual. We then secured the positive and negative probes together using a rubber band. Once again, the voltage source was set to 25V. To measure the electric fields, we put the negative probe on our equipotential, and the positive probe along the outer side of the curve. We then rotated the positive probe around the negative probe until we measured the largest voltage. This voltage was then recorded, and the position of the probes and direction of the electric field was marked on the carbon paper. The magnitude of the electric field was calculated by dividing the measured electric potential by the separation of the probe needles. The direction of the electric field was determined by the following manner: If the measured potential was positive, the electric field pointed towards the negative probe. If it was negative, it pointed towards the positive probe. For the second part of the lab, we switched out our piece of carbon paper with one that had metallic paint around all 4 edges. A dot of paint which the positive voltage was applied to was situated in the center of the paper. This setup can be seen in figure 2. The carbon paper was secured in the same fashion as before, and a hook was once again screwed into the dot of metallic paint. The positive terminal of the voltage source was once again attached to the metal screw, and the negative terminal was attached along the edge. The voltage source was set to 25V when taking measurements. The electric potential and electric field was measured at 4 different points on the carbon paper. The potential and electric field was measured using the same techniques mentioned above. The points that were measured were marked on the carbon paper with a colored pencil. Afterwards, the hook was removed from the carbon paper, and the distance between where the hook was screwed and the center of each of our voltage measurement points was measured using a ruler. Once again, there was some uncertainty added to our measurements because we had a difficult time marking the exact area that the probe touched the carbon paper with the color pencil. But in hindsight, the effect of the error could have been decreased by marking the measurement points beforehand, and then placing the probe in the center of each point when measuring the potential.

3 Figure 2 A diagram showing the layout of part 2 of the lab. Metallic paint was applied to the entire outer edge of the carbon paper and grounded. The positive paint charge was placed in the center of the carbon paper. Image taken from lab manual. Data Digital images of the pieces of carbon paper that I took my data on are attached to the end of this lab report. For relation between equipotential curves and electric field vectors, the original electric field vectors that were drawn with the colored pencils were pointed the wrong direction. However, I drew over them, so they are pointing in the correct direction (outwards). Also, I did not write the potential of the outer most potential on the piece of carbon paper, which was ± 0.05 V. Finally, there is one electric field line drawn on the carbon paper (solid line). However, it was not needed. For electric field and potential of a point charge, and equipotential line at our furthest out data point. This is also an extraneous piece of data. The measured values taken in electric field and potential of a point charge are shown in the table below: Point Label Distance From Center (mm) Potential Relative To Center (V) Voltage Between Probes (V) 1 23 ± ± ± ± ± ± ± ± ± ± ± ± 0.02 For all two probe measurements, the distance between the probes was: 10 ± 0.5 mm

4 Calculations The electric field was calculated using the following equation: E = V d Where V is the potential difference between the two probe needles and d is the distance between the probe needles. The uncertainty of the electric field magnitude was calculated by the following equation, which was given to us by our TA: E = ( V 2 d ) + ( V 2 d 2 d) Where V is the uncertainty in our potential measurement, d is the uncertainty in our distance measurement, V is the potential difference between our probes, and d is the distance between the tips of the probes. A sample calculation which uses my data is: E = V d ( 3.20 V) = m = 320 V m E = ( V 2 d ) + ( V 2 d 2 d) = ( 0.01 V m ) 2 = 8.1 V m V + ( (0.010 m) m)

5 Results My results from relation between equipotential curves and electric field vectors are shown in the following table: Equipotential Voltage ( V ) Vector Potential Between Electric Field Label Needles ( V ) Magnitude ( V/m ) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 4 When finding the electric field lines, I found that they were orthogonal to the equipotential lines and that they pointed towards the edge of the carbon paper. I was able to figure out the direction of the field lines because the probe needles using the method mentioned in my procedures section. A table showing the electric field found in the electric field and potential of a point charge is shown below, along with its relationship to its distance from the point charge. Vector Label Electric Field ( V/m ) Inverse Distance (m 1 ) E*r ( V ) ± ± ± ± ± ± ± ± ± ± ± ± 0.33

6 A plot of potential vs ln (r) can be seen below: Where r is the distance between the measure point on the carbon paper and the center of the carbon paper where the positive charge is being applied. As expected, the potential is proportional to ln r. The explanation for why the potential is proportional to ln r is outside of the scope of this course, so I do not know why that is the case. However, the reason we expect the electric field to be proportional to 1 r is because the electric field is equal to the derivative of the electric potential, and we know that the derivative of ln r is 1 r. Discussion In this experiment, we looked at two configurations where a positive voltage was applied to a piece of carbon paper, while one or all edges of the carbon paper were kept grounded. In these configurations, we measured the electric potential and electric field at different points on the paper. We compared the direction of the electric field lines with the equipotentials that they intersected and looked at how both values changed as we measured them further from the positive voltage source. In this experiment, there were multiple sources of uncertainty and error which effected our results. The first source of uncertainty was the precision of our measurement devices. The distances were measured with a short ruler which had a resolution of 0.1 mm, and the current was measured with an ammeter which could not display more than 4 significant figures at a time. We were able to quantize both uncertainties in our experiment and used them to define the uncertainty

7 on each of our measurements. However, these uncertainties can be decreased by using a caliper rather than a traditional ruler, and by using a more precise ammeter There were also some sources of uncertainty which we were not able to account for when taking our measurement. One of these are the edge effects of the metallic paint which is used to ground the edges of the carbon paper. In this experiment, we assume that the paint is applied as a perfectly uniform strip along one or all edges of the paper. However, that is not the case. Because the paint is applied with a brush, the edge of paint is actually quite jagged and non-uniform. This causes the 0 V equipotential to no longer be a straight line, and cause voltage measurements taken close to the paint to not behave as expected. However, this source of error could be fixed if we applied a piece of painter s tape on the carbon paper, applied the paint, and then removed the painters tape. This would create a smooth line along the edge of the conducting paint. Another source of error in this lab would be the resistance of the carbon paper. In this lab, we assumed that the carbon paper acts as a perfect conductor. However, the carbon paper actually has a resistance associated with it. That will cause some of the voltage to be converted into heat as it travels across the plane. However, we assume that there is no voltage being lost in this way when measuring the electric field. This would cause our electric field measurements to be larger than their actual values. This effect could be improved by using a better conductor as our surface when measuring the electric potential. Overall, the concepts studied in this lab have a huge impact on modern society. Potential differences are the driving force of electricity. As a simple example, flashlights can turn on because one terminal of its battery is at a higher voltage than the other. However, this lab also has the less overarching purpose in that it helps us better visualize the concepts that we are learning in the lectures. In a way, electricity is a lot like gravity. We have forces acting between objects which are not touching, and a potential associated with the distance between them. However, it is much easier to have a conceptual understanding of gravity because we are able to constantly see its effects. This lab gives us a chance to build that same type of visualization with electric fields.

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