PCS130 Lab Report #1 (1)

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Toronto Metropolitan University *

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130

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Physics

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Dec 6, 2023

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Faculty of Science Department of Physics Course Number PCS 130 Course Title Physics II Semester/Year Winter 2023 Instructor Tetyana Antimirova TA Name Sukhraj Virdee Lab/Tutorial Report No. Lab Report #1 Report Title Magnetic Fields Section No. 03 Group No. 59 Submission Date 02/02/2023 Due Date 02/02/2022 Student Name Student ID Signature Hodo Wardheer ****58201 H.W. Amber Bittle ****54827 A.B.

Introduction: The objective of this lab was to investigate the magnetic field of electrical coils and how change in various variables (position and current) can affect it. Current ( I ), describes the amount of energy (volume of electrons) flowing down a potential gradient and is measured in amperes (A) ( Zemaitis et al., 2022). The flow of currents are directed along a particular path and direction using conductive materials like such metals. Charge configuration is a significant factor in determining the magnetic field produced by electrical currents. In this lab, two electrical setups were utilised: a single coil and a double Helmholtz coil. A vernier sensor probe was used to detect the magnetic field at the centre of a single coil, throughout the axis of a single coil, and through the centre axis of two coils. As the experiment was performed variables were altered to determine their effect on the magnetic field. LoggerPro software and Microsoft Excel sheets were used to generate graphs and store data. By manipulating the distance of a probe and intensity of the currents, the magnetic field could be observed and their relationship could be further investigated and understood.

Theory: Magnetic Fields are produced by electric currents, which can be macroscopic currents in wires, or microscopic currents associated with electrons in atomic orbits (Hyperphysics, 2022). The magnetic field is often visualised through magnetic field lines, or lines of force, that leave one end of the magnet, arc through space, and re-enter the magnet at the other end (GOC, 2019). The Helmholtz coil is an electromagnetic apparatus consisting of two identical coils in which they are placed at the same distance from each other as their radius and have a region with a nearly uniform magnetic field (Virtuelle, 2022). Image retrieved from: https://virtuelle-experimente.de/en/b-feld/b-feld/helmholtzspulenpaar.php To properly investigate the magnetic fields created by electric current, the Biot-Savart Law was utilised. The Biot-Savart Law is an equation created by scientists Felix Savart and Jean Baptiste Biot. It describes the magnetic field with relation to its direction, length and proximity of the electric current produced and can be used for long straight conductors, or single/Helmholz coil. The direction of the magnetic field can be determined by using the right hand rule. In the equation, dB represents the magnetic field, I represents the electric current, r is the distance away from the conductor, n is the number of turns in a coil, and the constant represents the vacuum µ 0 permeability (classical vacuum definition: μ0 = 4π × 10−7 H/m) . Biot-Savart Law: ?? = µ 0 4π 𝐼(?𝐿 × ?) ? 2 The magnetic field near a long, straight conductor is represented as the equation: ? ?𝑖?? (𝐼, ?) = µ 0 𝐼 2π 1 ? θ

The magnetic field near a circular loop of wire is represented as the equation: ? ???? (𝐼, ?) = µ 0 𝐼 2 𝑅 2 (? 2 +𝑅 2) 3 ? The magnetic field for the Helmholtz coil is represented as the equation: ? = µ 0 𝑁𝐼 𝑅 8 5 5 Since the strength of the magnetic field can be influenced by variables such as position and current, it can be assumed that they are directly proportional to one another (as one increases/decreases it is reflected in the other). For this experiment, a vernier magnetic field sensor (probe) was used to measure the magnetic field at the centre of a single coil and throughout the central axis of a single and double coil. The position and current were manipulated throughout the experiment to observe the effect of position and current intensity on the magnetic field. Utilising the variations of equations provided, the magnetic fields for each of the experiments were determined and the corresponding graphs were generated to visualise the relationship . Finally, the percentage error was also determined by utilising the equation: Percentage error = 𝐹𝑖?𝑎? − 𝐼?𝑖?𝑖𝑎? 𝑖?𝑖?𝑖𝑎? | | × 100.

Procedure: The following paraphernalia required to perform the laboratory experiment were gathered. a) Power Supply b) Retort stand c) Ruler/Holder d) 2 × Magnetic field coil [200 turns, 10.5cm radius] + base e) Electric cables f) Vernier LabPro g) LoggerPro h) Vernier magnetic field sensor i) Clamps j) Elastic Bands Part 1- Magnetic Field at the Centre of a Single Coil: Firstly, the magnetic field sensor was connected to the LabPro interface. The field sensor was then calibrated using the zero function. Before turning on the power supply, a single coil was connected to it using the white plugs provided. The right hand rule was then used to confirm the direction of the coil's magnetic field. The sensor was set to 6.4 mT in range and the probe was positioned at the end of the metre stick, where it was perpendicular to the coils central axis point. While keeping the power supply off, the sensor was zeroed to remove the effect of any magnetic source. The power supply was turned on and set to 0.4 A. The play button was pressed and results were measured and recorded for a 10 second period. Observing the magnetic field vs. time graph generated by LoggerPro, the function analyse—> statistics was selected. The mean, standard deviation, magnetic field, electric current ( I ) and uncertainty results were recorded in the corresponding excel sheet provided. The process was repeated by increasing the magnetic field by 0.2 A till a maximum of 2 A. The relationship between the B coil (magnetic field of a single coil) and I (electric current) were plotted and a linear fit was applied for future analysis and reference. Part 2 - Magnetic Field along the Central Axis of a Single Coil: The power supply was turned off. The magnetic field sensor was zeroed while maintaining its position in the centre of the coil. The power supply was turned on and the current was set to 2 A. The metre stick and probe were moved away from the coil so that it remained at 20% of its maximum magnetic field (as observed in Part 1). Beginning at that position, the LoggerPro software was used to observe the magnetic field and position along the coils central axis. The

ruler and probe were moved 2 cm at a time until the initial magnetic field strength was reached on the opposite side of the coil. The results as well as the uncertainty value for the magnetic sensor were recorded in the excel sheet provided for future analysis. Part 3 - Magnetic Field of a Two Coils: The power supply was turned off and the magnetic field sensor was zeroed. The two coils were positioned parallel to one another and screwed in tightly to avoid movement. The plugs were connected to the other coil in correspondence with the right hand rule. The power supply was turned on and set to output a current of 1 A and an excel sheet named “Helmholtz Coil '' was created to record the results. The metre stick and probe were moved away from the coil so that it remained at 20% of its maximum magnetic field. Beginning at that position, the LoggerPro software was used to observe the magnetic field and position along the two coils central axis. The ruler and probe were moved 2 cm at a time until the initial magnetic field strength was reached on the opposite side of the two coil system. The equation for the magnetic field of the two coils was created and recorded for future use. The results as well as the uncertainty value for the magnetic sensor position were recorded in the excel sheet provided for future analysis. Part 4- Saving Data: The radius of the loops, number of turns, distance between the loops, and the excel files with recorded data were saved and stored for further analysis.

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