Electric and Potential Fields Lab Report PDF

Preview

Summary

Analyze the effects that a conductor and insulator have on a series of charged bodies from electric and potential fields....

Description

Danny Stein PHYS 1440L – 812 Robert Martin 6 February 2018 Partner: Louis St Onge Electric and Potential Fields

Objective: Analyze the effects that a conductor and insulator have on a series of charged bodies from electric and potential fields.

Introduction Every charged particle has a region surrounding it, known as the electric field, where forces are exerted on other charged particles. The vector electric field, 󰇍E, can be calculated by using the electric force, F󰇍, and the charge, q, which can be represented by: 󰇍E = F󰇍

q

1)

Electric field lines are imaginary force lines that are drawn tangential to any point within the electric field and are used to indicate the direction of the electric field. When a charged body gives off a field, it may not just be a vector electric field. Instead, it could create a scalar potential field (V). However, both types are very similar, but the electric potential difference, dV is the change in potential energy per unit change. When dealing with SI units, the electric potential difference is characterized as a volt and is shown in the equation: dV = −E󰇍 . ds

2)

where ds is a small displacement under the influence of the force. The electric potential travels over a surface, commonly known as the equipotential surface. When a series of points have a similar potential form, an equipotential line is created. Multiple equipotential lines are used to describe the potential field of the charges. If a displacement at angle ∅ occurs on one of the equipotential lines, then a change in potential energy is zero as a result of no work being performed. This proves how the electrostatic force, as well as the electric field, must be perpendicular to all the equipotential lines. Apparatus and Procedure Equipment 

Corkboard



DC Regulated Power Supply



Voltmeter



Conductive Paper



Printer Paper



Two Voltmeter Probes



Three Electrodes



Insulator Rod

Figure 1: DC Regulated Power Supply

Figure 2: Corkboard & Paper Setup

Procedure

Align the printer paper and conductive paper with the pins on the corkboard and punch holes to allow the pins to fit. Place the printer paper on the corkboard, and then place the conductive paper on top. Attach the metal conductors and tighten enough to hold both papers in place. Attach one probe from the voltmeter to the power supply. Attach the second probe from the power supply, and grip it onto the left electrode. Turn on the voltmeter and switch it the label “V”, and then turn on the power supply and set the output to 20 volts. Touch the probe to each of the metal conductors. The very left should read 20V, the middle around 10V, and the right should be 0V. Take the probe tip from the probe connecting the voltmeter and power supply, and place it on the conductive paper near the left electrode and make a small indentation. Record the voltage and move the probe and mark each spot with the same voltage (markings should be about an inch apart from each other). Repeat for eight separate voltages across the conductive paper. Connect the holes, remove the probe connecting the power supply and the electrode, and replace it with the insulator rod. Place the rod on the first voltage line, and use the probe tip to trace around the circumference of the rod, marking the highest voltage. Move the rod onto the most recent puncture, and repeat across the conductive paper.

Results and Analysis Results The white lines shown in Figure 3 were drawn by connecting all of the similar voltages. These lines demonstrate the equipotential lines. The voltages from left to right read 17.5 mV, 15.0 mV, 13.0 mV, 11.0 mV, 9.0 mV. 6.5 mV, and 3.5 mV. Opposite to the equipotential lines is the electric field, which are represented by the red and yellow lines. These lines were found using the highest voltage at each point, which ultimately formed a perpendicular line through all the equipotential lines. Analysis The equipotential line closest to the left electrode clearly shows to have some curving motion to it. Since this line is very close to the electrode, the path of it will always be small. However, once the lines get further away from the electrode, they begin to appear vertical with no curving motion to it. If the paper was extended, then it could easily be recognized that these lines would just be following a much larger circular path. The middle lines demonstrates what happens when an equipotential line approaches another electrode. The lines begin to wrap around every electrode in its general vicinity. The electric field lines show the path it takes to travel from one electrode to the next. After the first electrode, they begin to bend towards the second to allow for the field to remain perpendicular to equipotential lines.

Figure 3: Raw Data Collected on Conductive Paper

Discussion The results from this experiment proved to be true to its theory. The equipotential lines and electric field both followed their expected paths, resulting in them being perpendicular to one another, as well as curving around the electrodes on the paper. However, some areas were shown to have the intersection of the two lines to noticeably be off from the perpendicular 90 degrees. Each location on the equipotential lines were marked at the same voltage as other spots on the line. Considering the difficulty of finding the exact location, a tolerance of ± 0.03 mV was given to each location. The maximum voltage may not have been recorded when going around circumference of the insulator rod, which could also affect the results. Arguably the most obvious uncertainty would be having unwanted objects placed on the conductive paper. While marking many of the spots, a hand was placed on the paper, which could drastically affect the results. Conclusion This experiment was successful in expressing the relationship between equipotential and field lines, as well as the interaction they have with conductors to allow them to remain perpendicular to each other.

Questions 1) The electric field must be zero inside a conductor in electrostatic equilibrium because if the electrons within a conductor experience motion, they would experience some force, which would prevent them from being in electrostatic equilibrium. Our measurements support this because the conductor showed to have an electric field of zero. 2) Electric field lines cannot intersect each other they cannot travel in two directions at once. If they cross paths, then there would be two different values causing the same individual direction. Similarly, two equipotential lines cannot cross either because there would be two potential values at the same location....