Physics Laboratory Report part 11

Physics Laboratory Report Title: Magnetic Field of Helmholtz Coils— Biot-Savart Law Lab number and Title: lab 210 Name: Moe Jawish Group ID: 6 Date of Experiment: 11/14/2023 Date of Submission: 11/28/2023 Course section & section number: 121A-005 Instructor’s Name: Punyakanthi Sandeepani Thilakaratne Partner’s Names: Patrick Kearney, Andrew Dalmedo, Justin Andree Lo 1. Introduction: - Objectives: - The objective of this experiment was to understand the equations of the Biot-Savart law about magnetic field created by a circular current loop (coil). To measure the magnetic field strength of a single coil and a pair of coils as a function of the axial distance from the center of the coil. To study the magnetic field on the axis of a coil and relate this to the geometry of a coaxial pair of coils applying Biot-Savart law. - Theoretical Background: - Point P is situated along the axis of a single turn wire loop, positioned at a distance x from the loop. According to the BIot-Savart law, the magnetic field B at point P, generated by the loop with a radius R and current I, is expressed as follows: - B=m_0 IRsin(theta)/2r^2 - Here, I represents the current in the single turn coil m_0 is the permeability of air, and, r, R, theta are defined parameters. The Magnetic field B is formulated as a function of x: - B(x) = m_0 NI/R^2 2/(R^2+x^2)^3/2 - If we connect two coaxial coils with a separations of D, each having N turns and carrying currents I in the same direction, the total magnetic field B_net at point P on the axis is the sum of the vectors B_1 and B_2: - B_net = B_1(D/2 + x)+B_2 (D/2 + x) 2. Experimental Procedure: - Equipments: - Coils - Magnetic field sensor - Wooden track - DC power supply - Lab Jack - Coil Base - Ruler

- Universal Interface - Rotary Motion Sensor - Compass - Multimeter 3. Results: - Current (A) through the coilfor case I 0.2A 0.4A 0.6A Magnetic field strength (T) 0.5910x10^-4 1.171x10^-5 1.755x10^-5 -

4. Analysis and Discussion: - What is the relationship between coil current and magnetic strength that you have measured? - As the electric current rises, the strength of the magnetic field concurrently increases, demonstrating a direct proportional relationship between the two. - Does the theoretical plot fit everywhere over the experimental plot on the graph? - The experimental graph closely resembles the theoretical plot, exhibiting similar shapr. While not a perfect match at every point there is an overall consistency in their patterns. - How does changing the coil separation affect the magnetic field? What coil separation creates the most uniform magnetic field between 2 coils? Explain why the Helmholtz arrangement (D=R) is different than the other ones? - As the separation between the coils widens, the magnetic field strength increases, but it diminishes when positioned between the coils. For instance, in the graph depicting D=1.5R, the magnetic field shows an increase when moving away from the coils but decreases when located between them. The graph for D=R assumes the shape of an inverted hyperbola. This is a result of the coils being closer together, creating a more extended and uniform magnetic field. The graph for D=0.5R exhibits a similar shape but is considerably narrower. Consequently, the D=R configuration, known as the Helmholtz arrangement, yields the most uniform magnetic field between the two coils.

5. Conclusion: - I discovered that when the coils are positioned in close proximity and overlap, they generate a more extended and uniform magnetic field. Additionally, I gained a comprehension of the Biot-Savart Law equations governing the magnetic fields produced by a coil. The experiment utilized MATLAB and Pasco Capstone for data analysis, successfully validating the specified objectives. No uncertainties or questions arose during the course of the experiment.