EXP 16 copy

Experiment 16 Electric Field and Electric Potential Charles Williamson and Samantha Blumstein Abstract The purpose of the experiment was to study the electric field lines of various electric potentials between two electrodes. The experiment yielded electric field and electric potential measurements that were compared to the theoretical values. Investigation 1 found an electric field value of 76.75 V/m + 5.08 compared to the theoretical value of 100V/m. Investigation 2 determined electric field and electric potential values at each equipotential line. Discrepancies between the measured and theoretical values can be sourced to high error equipment and human error in measuring electric potentials. Introduction The purpose of the experiment is to study electric potential and electric field between electrodes in order to establish a relationship between them. Both describe the forces between charges however, electric potential describes the scalar quantity of energy between charges while the electric field describes the vector value of the forces between the charges. Investigation 1 examines the electric potentials and electric field distribution of a parallel plate capacitor. Two parallel electrodes, representing negative and positive terminals, create an electric field. Investigation 2 examines the electric field between concentric electrodes. Measurements of the electric field generated electric potential lines. Investigation 1 To begin, on a conducting rubber pad, two parallel electrodes were parallel placed 10 cm apart. The electrodes were connected to the power supply at 10V. A probe tipped wire was connected to the V input of the voltmeter. This probe was then used to find equipotential lines of voltage of 3-7V. With each voltage, many points were marked and then connected to display the equipotential lines. Figure 1: Plot of Electric Potential vs. Position 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0 2 4 6 8 10 12 f(x) = 0 Voltage vs. Position X Position x (m) Voltage (V)

The slope of the best fit line in Figure 1, 76.749 (V/m) is the measured electric field. The theoretical electric field was 100 V/m. The electric field error of 5.08 V/m was found using the online error calculator. The measured electric field did equal 100 V/m at the 6 V potential but steadily decreased as shown in Figure 2. Figure 2: Electric Field vs. Position x The electric field was measured by using the equation below. This data was plotted against the position data to generate the graph above. Investigation 2 To begin, a solid concentric electrode was placed in the middle of a larger hollow concentric electrode. The radiuses of each electrode were measured. The smaller electrode, a, equaled 0.01m and the larger electrode, b, equaled 0.106m. The outer electrode was connected to the negative terminal and the positive to the inner electrode. The power supply was set to 10V and the probe tipped wire was connected to the V input of the voltmeter. The voltages, 2-6, were marked every 45º around the inner electrode and connected to create concentric equipotential lines. Volts R avg. Theoretical V E (V/m) 1/r Theoretical E 6 0.026 5.95 114.29 38.46 162.91 5 0.03475 4.72 142.86 28.78 121.89 4 0.04175 3.95 93.02 23.95 101.46 3 0.0525 2.98 70.18 19.05 80.68 2 0.06675 1.96 14.98 63.46 The distance from each equipotential line to the center electrode was measured and averaged in order to make several calculations. 0.02 0.02 0.03 0.03 0.04 0.04 0.05 0.05 0.06 0.06 0.07 0 20 40 60 80 100 120 Electric Field vs. Position X Position (m) Electric Field (V/m)

field was measured as 76.75 V/m + 5.06 compared to the theoretical value of 100 V/m. The experimental electric field value was not within the calculated error indicating experimental error. Investigation 2 studied the electric field between concentric electrodes. This generated electric potential and electric field calculations that were also compared to their theoretical values. The experimental values differed greatly from the theoretical values indicating further sources of error. Questions 1. If the potential difference ∆V were doubled, then the electric field would double because the two are proportional. 2. The errors within the paper and the electrodes would be systematic errors. 3. The electric field begins to decrease as the the equipotential lines leave the space between the electrodes because the lines begin to drift away from the center. 4. Based off the formula E=∆V/d, if the distance is halved, then the magnitude of the electric field would double. 5. Based off of formula in INV 2, if the diameter of the outer ring is doubled, then the magnitude of the electric field would also be halved.