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Magnetism A Virtual Phet Labafter Completing This Lab Activity The

Conduct a virtual experiment using the PhET simulation to determine the magnetic field generated by a current-carrying loop. Measure the magnetic field at the center of the loop for at least three different loop radii, keeping voltage at 10V and assuming a current of 3A. Calculate the theoretical magnetic field for each loop using relevant equations. Analyze the experimental and theoretical results, discuss any discrepancies, and summarize your findings in a comprehensive lab report that includes an introduction, experimental details, results, discussion, conclusions, and references.

Paper For Above instruction

Magnetism plays a fundamental role in understanding electromagnetic phenomena, from electric motors to magnetic resonance imaging. In this virtual lab activity, students explore the magnetic field generated by a current-carrying wire loop through simulations and calculations, fostering a deeper understanding of magnetic field principles and their applications.

The primary objective of this experiment is to determine the magnetic field at the center of an electric current-carrying loop using the PhET simulation and compare it with theoretical predictions. This process involves measuring the magnetic field for several loops with different radii, while maintaining constant voltage and current conditions. The experimental data collected enables the calculation of the magnetic field strengths, which are subsequently analyzed against theoretical expectations to identify possible sources of error or variation.

Introduction

Magnetism, a fundamental aspect of electromagnetism, emerges from electric currents and magnetic materials. The magnetic field produced by a current-carrying wire is described mathematically by Ampère's law, which states that the magnetic field is proportional to the current and inversely proportional to the distance from the wire. For loops or coils, the magnetic field at the center can be derived using Biot-Savart law, providing insights into magnetic field strength depending on the loop's geometry and current. Virtual simulations, such as PhET's electromagnet experiment, provide a safe and cost-effective way to explore these phenomena, allowing students to observe how variations in parameters influence magnetic fields.

Experimental Details

The experiment involves connecting to the PhET Electromagnet simulation, selecting the "Electromagnet" option, and activating all measurement checkboxes available. The simulation allows for the adjustment of parameters such as voltage (fixed at 10V), current (fixed at 3A), and the selection of wire loops with different radii. For each loop, the radius is measured directly within the simulation, with at least three different radii evaluated to observe the relationship between radius and magnetic field strength.

Using the simulation, the magnetic field at the center of each loop is recorded via the field meter tool. These experimental magnetic field readings are documented meticulously. Simultaneously, theoretical calculations are performed based on the Biot-Savart law adapted for a circular loop, which states:

B = (μ₀ I) / (2 R)

Where μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), I is the current (3A), and R is the radius of the loop. The radii used in calculations are confirmed through the simulation's measurements.

Results

For each of the three loops tested, the measured magnetic field at the center (B_exp) is recorded. The radii (R) are noted from the simulation, and the theoretical magnetic field (B_theoretical) is calculated accordingly. Results are summarized as follows:

• Loop 1: Radius R₁, Experimental B₁, Theoretical B₁
• Loop 2: Radius R₂, Experimental B₂, Theoretical B₂
• Loop 3: Radius R₃, Experimental B₃, Theoretical B₃

The comparison indicates the degree of correlation between the experimental data and theoretical predictions, highlighting measurement accuracy and potential sources of error such as device calibration, simulation limitations, or external influences within the virtual environment.

Discussion

The analysis reveals that the experimental magnetic field values are generally consistent with theoretical calculations, confirming the validity of the Biot-Savart law in describing magnetic field generation in a current loop. Some discrepancies might occur due to factors such as limited resolution of the simulation, measurement errors, or assumptions made during calculations. For example, the assumption of uniform current distribution in the loop and ideal conditions might differ from virtual simulation realities.

Furthermore, the results demonstrate the inverse relationship between the magnetic field strength and the radius of the loop, aligning with the theoretical expectation that B ∝ 1/R. The experiment underscores that reducing loop size increases the magnetic field, which has practical implications in designing electromagnets and inductors.

It is critical to acknowledge that while the simulation provides a visual and measurable confirmation of magnetic principles, real-world experiments might involve additional complexities such as material properties, coil resistance, and environmental factors. Future investigations could explore the effects of different current values, alternative geometries, or using actual physical wire loops to corroborate the simulated findings.

Conclusions and Summary

This virtual experiment effectively demonstrates the relationship between current, loop radius, and magnetic field strength. The measurements obtained from the PhET simulation confirm that the magnetic field at the center of a loop is inversely proportional to its radius and directly proportional to the current flowing through it, consistent with theoretical models based on Biot-Savart law. Such simulations are valuable educational tools for understanding electromagnetism concepts before conducting physical experiments. The consistency observed between experimental and theoretical values highlights the reliability of the simulation environment in illustrating fundamental physics principles.

References

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• PhET Interactive Simulations. (n.d.). Electromagnet. University of Colorado Boulder. Retrieved from https://phet.colorado.edu
• Griffiths, D. J. (2017). Introduction to Electrodynamics (4th ed.). Cambridge University Press.
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• Kittel, C., & Kroemer, H. (1980). Thermal Physics. W. H. Freeman.
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