Lab 5

pdf

School

Texas A&M University *

*We aren’t endorsed by this school

Course

217

Subject

Electrical Engineering

Date

Dec 6, 2023

Type

pdf

Pages

Uploaded by CoachFlower10294

LAB 5: L ORENTZ F ORCE Stephen Adcox, Jayden Rodriguez, Yildiz Ulugun Texas A&M University College Station, TX 77843, US. Abstract : This report covers the general theory behind Lorentz Force. Using the load cell, a calibration curve is made after measuring multiple voltages as the mass increases. These measurements are used to compute the Lorentz Force after measuring the voltages as current increases in a coil. Furthermore, the data measured and calculated are graphed two-dimensionally which will allow for the computation of the Magnetic Field and its uncertainty along with knowing the length of the load cell and the number of turns in the coil. This exercise’s purpose is to measure the strength and the direction of the magnetic field between magnets. Keywords: Lorentz Force, Voltage, Load Cell, Magnetic Field 1. Introduction Throughout the experiment, the group will gain an understanding of the Lorentz Force. Lorentz Force describes how charged particles move under the influence of electric and magnetic fields and experience a magnetic force that can be quantified by: Equation 1 ? → = ?? → × ? → + ?? → In the equation, is the force on the particle, is the charge on the particle, is the velocity of the ? → ? ? → charged particle, is the magnetic field vector, and is the magnetic field present. ? → ?? → Load cells are used to determine the calibration curve. The load cells output a voltage that is proportional to the force applied meaning that more weight will correlate to a higher voltage value. There are two load cells on each apparatus therefore the following equation needs to be used: Equation 2 𝑉 ??? = 𝑉 ?ℎ 4 + 𝑉 ?ℎ 5 In addition, assuming the load cells have a linear response the following equation is used to find the and ? 1 values: Equation 3 ? 2 𝑉 ?????? = ? 1 ? 𝑎???𝑖?? + ? 2 In the equation, is the dependent variable, is the slope, is the independent variable, and 𝑉 ?????? ? 1 ? 𝑎???𝑖?? is the y-intercept for the plotted graph according to the line of best fit. ? 2 To measure the Lorentz Force, load cell output is measured as current serves as the independent value. This allows for the calculation of Lorentz Force by applying the calibration curve to the voltage affected by the change in current. Equation 4 ? 𝐿 = 𝑉−? 2 ? 1 Where is the Lorentz Force, V is the at the specified point, and / are the calibration values ? 𝐿 𝑉 ?????? ? 1 ? 2 A magnetic field is a vector field that describes the magnetic influence on moving electron charges and electric currents. The magnitude of the magnetic field can be calculated from the Lorentz Force. Equation 5 |?| = ? 𝑁? Where B is the magnetic field, m is the slope of as a function of the Current graph, N is the number of ? 𝐿 loops of the wire, and l is the length of the load cell. The standard error equation allows for the calculation of the uncertainty of measurements. In this case, the uncertainty is being calculated for the Magnetic Field. Many known and unknown errors could affect the final value which leads to uncertainty. Equation 6 𝑆? = σ 𝑁 Where SE is the Standard Error, is the sample standard deviation, and N is the number of samples σ

2. Experimental Procedure Various parts of the experiment would eventually lead the group to find the magnetic field of the coil. Before starting the experiment, MobaXTerm had to be loaded and a computer connected to the DAQ. We started by establishing the calibration curve for the load cell after setting up our setup, which involved assembling the orange rectangular apparatus, putting up weights, the Data Acquisition (DAQ) system, and using the Python scripts that were provided. The procedure was adding different weights to the device in increments of 10 g, from 0 g to 150 g. Following this data collection, we could create a graph showing the relationship between the voltage output and the applied force (mass × gravity). Next, the orange device was positioned beneath a suspended coil of wire. The Python script was run to record the output voltage after an electrical current was run by the wire up to a maximum of 0.5 A. From 0.01 A to 0.15 A, the current was systematically increased in increments of 0.01 A. Data records were maintained on an Excel sheet for each phase of the experiment. The team then computed the wire coil's magnetic field with the collected data and the formulas provided. To determine the total voltage, Equation 2 was used to calculate the total voltage outputted from channel 4 and channel 5. Next, the force applied was calculated by converting the mass to kilograms and multiplying by the gravity constant, 9.81. The total voltage and force applied data were graphed and a line of best fit was added. Comparing the trendline equation to Equation 3 , the calibration values of and were able to be determined. ? 1 ? 2 Using the total voltage gathered after incrementally increasing the current, Equation 4 was used to calculate the Lorentz force. The newly calculated Lorentz force and the current data were then graphed and a line of best fit was once again added. Equation 5 was now able to be used because the slope was the last unknown value to be able to calculate the magnetic field. The uncertainty was then calculated using Equation 6 . In addition, Equation 1 was used to help annotate the setup. 3. Results and Analysis: According to Figure 1 , there was a linear relationship between the Voltage vs Force which was the response that was assumed to have occurred. The relationship shows as the amount of weight increased, the amount of force increased which resulted in the total voltage output being increased coming out of both channels 4 and 5. The data was strongly correlated and the line of best fit gave the group the value of the slope and the y-intercept which corresponded to the calibration values of and found in Table 1 . This led to the equation of Lorentz ? 1 ? 2 Force which was implemented to the total voltage output values after incrementally increasing the current . Figure 1: Voltage vs Force on Load Cell Table 1: Calibration Values ? 1 𝑉𝑎??? ? 2 𝑉𝑎??? Equation 0.0004 0.014 ? 𝐿 = 𝑉−0.0014 0.0004

Figure 2: Calculated Lorentz Force vs Current Table 2: Values used for Magnetic Field Number of Loops of Wire Length of Load Cell (m) Lorentz Force/ Slope (N) Magnetic Field ( ) 𝑁 ?·? Uncertainty ( ) 𝑁 ?·? 200 0.08 -1.525 9. 53 × 10 −2 1. 38 × 10 −4 The Lorentz Force vs Current graph also shows a linear relationship. Due to the current being clockwise, the Lorentz Force is decreasing as the current increases. Therefore, the force on the coil is negative, having a downward force. The force on the apparatus is an upward force found from the right-hand rule. There was some uncertainty within our results. The incremental increase of the current was small and resulted in the total voltage values not having as strong of a correlation as the group would have hoped. This possibly affected the calculated magnetic field's value from its actual value. Figure 3: Annotation of the orientation Figure 3 shows the annotated setup of the experiment. The current is flowing in a clockwise direction because the red wire, voltage, is to the right of the black wire, ground, and the voltage leads to the ground. Using the Right Hand Rule where the current is flowing through the apparatus, the group can find the Lorentz Force acting on the apparatus. Current is flowing to the left at the apparatus, therefore the hand sticks to the left direction. The magnetic field is out so the fingers of the hand curl inwards. This results in the thumb being pointed in the upward direction. Therefore, the Lorentz Force on the apparatus is in the positive y direction. The Lorentz Force on the coil is what was calculated during the lab so the negative value calculated resulted in the force being in the negative y-direction. 4. Conclusions This lab required a basic understanding of Lorentz Force, Voltage, Load Cell, Current, and Magnetic Field to calculate the magnetic field around a group of wires with current flowing through. Using the load cells, we calculated the voltage through the wires. By finding the current change to the load cell output, we calculated the Lorentz Force. Finally, we derived the magnetic field's magnitude from this force. It was found that the magnetic field strength was 0.0953 Tesla. Errors in the voltage readings or human mistakes could have led to an inaccurate magnetic field value compared to our prediction. Numerous other factors could have also contributed to the uncertainty.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version