LabReportTemplatev6

.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

3

Uploaded by maye0618 on coursehero.com

LAB 5: L ORENTZ F ORCE Aakash Jain, Eli Louis, Marielva Salas Texas A&M University College Station, TX 77843, US. Abstract This report covers how to find the strength of a magnetic field using the Lorentz force. The students calibrated the load cells and used magnets separated by coils to measure the current. Current Load cells were calibrated and magnets were placed to measure the current flowing through the given apparatus. Once calibrated students used the DAQ for known output of current to the coil, this was part of the process to measure the Lorentz force. This lab allows familiarity with the given components to grow within the students. Keywords: magnetism, current, Lorentz Force, magnetic field, 1. Introduction This lab focuses on using a measured Lorentz force to calculate the magnetic field pushing against a magnetic apparatus which is connected to load cells. The load cells are calibrated using standardized weights, and then current is sent through the apparatus at a known level. Load cells are transducers that convert a mechanical force (in this case, the Lorentz force) into an electrical signal. Calibration is necessary to establish a linear relationship between the applied force and the electrical output of the load cell. Standardized weights are used to apply known forces to the load cells during calibration. Calibration coefficients (C1 and C2) are determined by measuring the corresponding electrical signals to relate force to voltage. Using Equation 1 students were able to calculate the magnetic field produced by the force and current. The cross product in the equation indicates that the force is perpendicular to both the direction of the current and the magnetic field. The right-hand rule is commonly used to determine the direction of the force based on the direction of the current and magnetic field, and also used to determine the direction of current and magnetic field. The constants known helps determine the magnetic field based on the following equations: Equation 1 𝐹 = 𝑃 ∮ 𝐼𝑑? × ? Where is the Lorentz Force with a negligible electric field, is the current, is the differential length of the coil, 𝐹 𝐼 𝑑? and is the magnetic field. ? Equation 2 𝑉 = ? 1 𝐹 + ? 2 Where V is the voltage, is the first calibration coefficient, is the second calibration coefficient, and is the ? 1 ? 2 𝐹 applied force. Equation 3 𝐹 = ?𝑔 Where F is the force, is the mass of the object, is the gravitational acceleration. ? 𝑔 2. Experimental Procedure First, the load cells were calibrated to accurately record the load cell output. This consisted of measuring fifteen different weights and the force applied by each of them. The load cells were then configured as depicted in Figure 1 and were used to measure the output as a function of current through the coil. To gather data to measure the Lorentz force, students used the DAQ to change the current output, using the DAQ the students increased their current from .015 A to .5 A, changing between fifteen output current values. Equation 2 was used to calculate the Lorentz force, and then using that plot, Equation 1 was used to calculate the magnitude of the magnetic field.
Figure 1: Experimental Set up 3. Results and Analysis We begin with analyzing our data to produce a relationship between applied current and the Lorentz force. The first step to produce this result was determining the calibration curve of the load cell. To calculate this, the masses placed on the load cell were converted to force using Equation 3 , and these resultant forces were plotted against the total voltage output of the load cell. By applying a linear fit to the data according to Equation 2 as shown in Figure 2 , we recover the calibration coefficients: and . ? 1 = 0. 0005 𝑉 𝑁 ? 2 = 0. 0017𝑉 Figure 2: Calibration Curve Figure 3: Measured Lorentz Force With the calibration curve we can analyze the data for the Lorentz force. Equation 2 is rearranged to solve for the force given a measured voltage, such that . This equation is applied on each voltage 𝐹 = 𝑉−? 2 ? 1 = 𝑉−0.0017 0.0005 measurement to find the force measurement for each current value. This is plotted in Figure 3 . Next we find the strength of the magnetic field based on the Lorentz force magnitude. We must begin with manipulating Equation 1 . First, we assume that each loop of the coil has negligibly similar conditions to each other loop. This allows us to solve the force for one loop, then multiply that force by the number of loops to get the total force, producing the equation , where N is the number of coils and the path C is over 1 coil rather 𝐹 = 𝑁 ? ∮ 𝐼𝑑? × ? than all 500. Next, we assume that current is constant through the wire, so . Finally, we assume 𝐹 = 𝑁𝐼 ? ∮ 𝑑? × ?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help