Electric Field and Electric Potential Lab Report

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Northeastern University *

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Electrical Engineering

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Feb 20, 2024

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Report for Experiment #16 Electric Field and Electric Potential Vaughn Montoya Lab Partner: Sen Niu TA: Ji Tae 2/17/2023

Introduction An electric field happens to be a vector force that encompasses an charged related to the forces between them. There happens to be one way to detect it which is to see if another charge experiences an repulsion or attraction in the field. Electric fields can be seen by electric field lines which point in the direction of the maximum field at that point. Electric field lines are at every point perpendicular to the equipotential lines. The strength of a force on a test charge is F=qE (1) where q is the test charge and E is the electric field. The potential field is a scalar field, which is giving just magnitude and the electric field is a vector field, which has both magnitude and direction. When connecting pieces of metal to two poles of a battery or DC power supply positive charges will accumulate on one of the pieces while the other will accumulate negative charges. These charges will make a potential field between the two pieces of metal. Then a ground, zero potential was set to one of the electrodes and compared the other points thereby making a map of potentials. A simple way to do this is to look for lines along the potential that stay the same which are known as equipotential lines. Electric field can be calculated by using the following equation: ࠵? ! = − ∆࠵? ∆࠵? = − ࠵? " − ࠵? # ࠵? " − ࠵? # (2) The objects of this lab were to look at the electric potential between two electrodes, and to figure out the relation between electric potential and electric field as well as to study electric field between electrodes. In the first Investigation a piece of black conducting paper was placed in the middle with parallel electrodes and lines drawn long the edges of the electrodes. They were then connected to a voltage source and equipotential lines were searched for between the electrodes. In this Investigation voltage happens to increase from negative to positive electrode and the electric field between the parallel plates remains approximately constant. A plot of V vs. X and E vs. x was made to visualize this theory. Investigation 2 used the same black conducting paper was used and two brass circular electrodes were used this time. In this Investigation static field in a coaxial cable, like those used to feed cable TV was stimulated to highlight that equipotential lines are curved. Plots of V vs. average radius and E vs. 1/࠵? $ were made to look at these theories. Investigation 1 The setup for Investigation 1 consisted of placing the rubber pad in the middle of the table and then placing the conducting paper on the top. Then two parallel plates were placed 10 cm apart from each other. A grease pencil was used to trace a line on the inside of the electrodes to highlight where they were. 10 V is what the power supply was set to and the connecting wires which were put in and attached and the plate on the left was set to x=0 also known as the grounding plate while the one on the right was set x=d. The scale of the voltmeter was set to read at 10 V. The probe was used to check that the positive plate, the plate on the right registered 10 V. Then equipotential lines were found in increments of 1V, the 5 V line was found first because towards the center should be parallel, a straight line. Then 2 V to 8 V was found using the probe and marked and labeled with a grease pencil. Also, the potential was found outside of the two parallel plates

known as the fringe field, where the electrode ends. One person was holding down on the parallel plates to ensure there was a solid connection while the other was doing the measurements. The 5v was then confirmed to be halfway between the two electrodes. Then perpendicular lines were drawn from the equipotential lines. Measurements between the equipotential line and grounded electrode were recorded. Half the thickness of line was determined to be the uncertainty of x which was simply just 0.0005m. Error in voltage was just 1% of the voltage value. The theoretical voltage V was found by using the following equation: ࠵? = |Ex | (3) of the Then Electric field, E was calculated between pairs of potential lines and its error was found using the following equation: ࠵?࠵? = ࠵? 4 ࠵?࠵? % ࠵? + ࠵?࠵? % ࠵? (4) Then the theoretical electric field was calculated by taking the absolute value of second equation in the introduction. Then the average position, ࠵? #&’ was found using the following equation: ࠵? #&’ = ࠵? # + ࠵? " 2 (5) Then its error was found using the following using the following equation: ࠵?࠵? #&’ = 1 2 8 2࠵?࠵? % (6) A table was made for the data in Investigation 1 Table 1: All data from Investigation 1: Vth= Theoretical Voltage and Eth= Theoretical Electric Field x (m) δx (m) V (V) δV (V) ࠵? #&’ (m) ࠵?࠵? #&’ (m) Ε (V/m) δE( V/m) Vth (V) Eth( V/m) 0.018 0.0005 2 0.02 0.032 0.0035 -100 -3.7 -1.8 -100 0.028 0.0005 3 0.03 0.047 0.0035 -100 -5.1 -2.8 -100 0.038 0.0005 4 0.04 0.064 0.0035 -71.4 -4.9 -3.8 -100 0.052 0.0005 5 0.05 0.083 0.0035 -111 -9.8 -5.2 -100 0.061 0.0005 6 0.06 0.098 0.0035 -83.3 -8.8 -6.1 -100 0.073 0.0005 7 0.07 0.11 0.0035 -125 -15.5 -7.3 -100

0.081 0.0005 8 0.08 x 0.0035 -98.8 x -8.1 -100 A plot of Voltage (V) vs position (X) was made to look at voltage as it increases from negative to positive electrode. Plugging the data into the IPL straight line of fit calculator, the experimental slope was found to be 92.0 ࠵?/࠵? ± 1.19 ࠵?/࠵? . The experimental slope did not fall within the theoretical slope. This could have been because of human error in measuring and drawing the equipotential lines. Figure 1: Voltage (V) vs. Position (X) A plot of E vs. X was made to look at and show that electric field remains constant between the two electrodes. Using IPL straight line of fit calculator, the experimental slope was found to be 165.0 ࠵?/࠵? % ± 107.2 ࠵?/࠵? % . The slope does not agree with the theoretical data which could be because of human errors such as not correctly measuring the distance between grounded potential and equipotential lines thus impacting electric field calculations. y = 92.444x + 0.3646 y = 100x 0 1 2 3 4 5 6 7 8 9 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Voltage (V) Distance (m) Voltage (V) vs Distance(X) and V Theoretical Expected Theoretical Linear (Expected) Linear (Theoretical) Linear (Theoretical)

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