Lab Report 1 - Electric Field PDF

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Julia Varricchio PHY 134 Section 07 Experiment 01: The Electric Field Experiment performed on: February 9, 2020 with Zifan Wang Report submitted: February 15, 2020

Introduction In this lab we examined the electric fields of a set of parallel plates and a dipole. Specifically, we studied the relationship of electric field strength, voltage, electric field lines, and equipotentials for these charge configurations. These relationships are indicated by the equations E(x2-x1 component)=

-(V2-V1)/abs(x2-x1). Qualitatively, these relationships show us how equipotential

lines and electric field lines are layed out in these charge configurations. We also examined the charge of electric fields. We utlizied the equation E=(kq)/r^2 in vector form to determine the charge of the electric field. Theory By examining the relationships in parallel plates and dipoles, we can see that electric field lines travel from positive to negative charges and are parallel to the electric field. They also are spaced out differently depending on the strength of the electric field. In particular, electric field lines are bunched closer together where the electric field is stronger, and are more spread out where the electric field is weaker. So, if we were to swap positive and negative charges in the dipole arrangement the electric field shape would stay the same. In other words the electric field lines would be parallel and the spacing between the lines would be the same. However, the direction of the electric field would be different. The electric field lines for a positive charge go outwards towards the negative charge, while for a negative charge they go inwards. Apparatus

Results

For the parallel plate configuration, we plotted the equipotential lines in order to find the shape of the electric field lines. This is demonstrated by the top figure. We arrived at the shape of the electric field lines from our knowledge that electric field lines are parallel to equipotential lines. We repeated this with the dipole configuration, which is shown by the second figure. After, drawing out the electric field lines of the parallel plate configuration, we also determined quantitatively the components of the electric field in the x2-x1 direction. We determined this by measuring the voltages of the center column and the distance between the point from the plate. These measurements were used in a voltage vs. position graph. This graph gave us a slope of 71.8493 +/1.74137. The slope from this graph represents the components of the electric field in the x2-x1 direction. We also quantitatively analzyed our dipole configuration by determining the charge on each pole. We expected the poles to be the same magnitude but opposite sign. In order to determine this we used the equation E  =(kq)/r^2. From our calculations we got a value of 1.65 x 10^-8 (+/- 0.00000000269)

for the high voltage pole and -1.75 x 10^-8 (+/-0.00000000288) for the low voltage pole. With uncertainties in mind, our measurements of the charge for the high voltage and low voltage pole are the same in magnitude but opposite in sign. Error Analysis Although we calculated uncertainties in our data, this does not account for systemic errors. Some errors that may have impacted the shape of our electric field lines are objects in the ambient environment that may have had a charge. If that was the case the objects may influence the shape of our electric field lines depending on the sign of the charge. Another possible source of error may be the voltmeter we used to measure voltage at each point. Lastly my partner may also be a source of error. In other words, we may have not plotted the exact point where the voltmeter read 0 for the equipotential lines. Discussion Questions

1. Alternative configurations If we were to swap positive and negative charges in the dipole arrangement the electric field shape would stay the same. In other words the electric field lines would be parallel and the spacing between the lines would be the same. However, the direction of the electric field would be different. The electric field lines for a positive charge go outwards towards the negative charge, while for a negative charge they go inwards. 2. Systemic Error Some errors that may have impacted the shape of our electric field lines are objects in the ambient environment that may have had a charge. If that was the case the objects may influence the shape of our electric field lines depending on the sign of the charge. Another possible source of error may be the voltmeter we used to measure voltage at each point. The voltmeter may not have had the most accurate reading of the voltage at each point. Lastly my partner may also be a source of error. In other words, we may have not plotted the exact point where the voltmeter read 0 for the equipotential lines.

3. Deviations from expected behavior A. Conductors: Although we expect the conductor to be a constant voltage throughout, we may observe a milivolts-ish difference between different points on it. We can relate this back to Ohm’s law. Ohm’s law states I=V/R, where R is constant. However, some conductive material does not obey this law. So, in our case R was not constant, so the voltage may be different between two points. B. Third Dimesion: We observe electric field lines in a two-dimensional space. They travel from positive to negative and mimic what would happen if there was a third dimension.

4. Qualitatively draw the electric field lines for a positive point charge q placed at a distance d from a conducting plate. The plate is at potential 0.

Conclusion From this lab we were able to see quantitatively and qualitatively the elements of an electric field. We noticed that the electric field lines always travel from positive to negative charges in a parallel line. These lines are also perpendicular to the equipotential lines. Equipotential lines are where the component of the electric field is 0. From our date we also, extrapolated the component of the electric field in the x2 - x1 direction for the parallel plate configuration as well as determining the charge of the poles in the dipole configuration. In order to make this experiment more accurate, we can perform it in a controlled environment. By controlled environment, I mean one in which there are no other electric fields or charged objects in the ambient environment that may influence the shape of our electric field....