A Quick and Intuitive Demonstration of (Magnetic) Resonance Using Just Three Magnets

The apparatus for our demonstration consists of three magnets: a bar magnet, a small compass, and a large compass, as illustrated in Fig. 1. To begin the demonstration, the bar magnet is first positioned in proximity to the stationary small compass. This placement causes the needle of the small compass to align in a specific direction, a result of the magnetic force due to the bar magnet. Subsequently, the large compass, which has no casing, is set adjacent to the small compass. The instructor then manually gives the large compass an initial velocity of rotation and asks students to observe the effects.

The combined system of the bar magnet and the small compass has a distinct natural frequency that is dependent on the properties inherent to the bar magnet, the small compass, and their relative placement. When the small compass is momentarily disturbed—such as bringing the large compass near and then retracting it—the compass needle starts to oscillate around its equilibrium. This oscillatory motion will soon be dampened due to air drag.

As the large compass rotates, its magnetic field (magnetic force) fluctuates. Specifically, at the position of the small compass, the magnetic field of the rotating large compass changes in both direction and magnitude. This periodic shift induces a corresponding change in the magnetic force exerted on the small compass, causing a jitter, or oscillating motion, of the small compass needle, as illustrated in Fig. 2(a). Air drag gradually slows the large compass’s rotational frequency, leading to a gradual shift in the driving force’s frequency. The small compass’s magnitude of oscillation varies in response to these frequency changes. When the rotating large compass’s frequency aligns with the natural frequency of the bar magnet–small compass system, the jitter reaches its peak amplitude [Fig. 2(b)]. As the rotating large compass’s frequency further decreases, the small compass’s oscillation amplitude diminishes [Fig. 2(c)].

In essence, as the rotation frequency of the large compass decreases, students observe a distinct rise and fall in the amplitude of the small compass’s oscillations. The entire demonstration is concise, concluding in roughly half a minute. After watching the demonstration, students are equipped to sketch the resonance curve qualitatively, showcasing how amplitude varies with driving frequency.

When the demonstration is presented to a large group of students in a classroom, a projection of it would help the students view it as the small compass is not easy to see from a distance. The large compass can be any sufficiently strong dipole magnet.

The use of air drag to gradually decrease the driving frequency of the field effectively demonstrates a frequency sweep in spectroscopy. Spectroscopy is a scientific technique used to analyze the interaction between matter and electromagnetic radiation. It’s a method that helps to understand the properties of substances based on how they emit, absorb, or scatter light (or other electromagnetic radiation) across various wavelengths. In a frequency sweep, one measures a physical quantity at a particular frequency and then methodically varies this frequency to record subsequent measurements. This process is iterated across a spectrum of frequencies, incrementally either increasing or decreasing them. The frequency sweep is a prevalent experimental technique in science and engineering, instrumental for investigating systems and materials with frequency-dependent properties.^10–12 Consequently, the natural slowing of the rotating large magnet, due to air drag, visually showcases the crucial concept of a frequency sweep to students, facilitating an intuitive observation.

Including the term “magnetic field” in this demonstration’s explanation is not essential. Students can grasp the physics through the direct interaction between the large and small compasses, both inherently magnetic. Hence, the concept can even be easily understood by those lacking a physics background. Yet, by integrating the notion of the magnetic field, this demonstration also doubles as an exemplary representation of both simplified nuclear magnetic resonance and ferromagnetic resonance.^13–15 In addition, if one mounts the large compass on a motor that allows for constant rotation, it sets a fixed driving frequency. One can then adjust the distance between the bar magnet and the small compass to perform a sweep of the natural frequency and use freeware apps for smartphones (e.g., phyphox) to aid the analysis. In ferromagnetic resonance, this is typically referred to as the field sweep (varying the external aligning magnetic field).¹⁶ 

The described demonstration can also be an experiment performed by individual students or used in an inquiry-based lab.¹⁷ In this case, the instructor begins the lesson by leading the students through an initial inquiry to answer the question about how to get higher on a swing push (pushing with an appropriate frequency). Next, the instructor guides the students through the main inquiry about the relationship between the amplitude of forced oscillation and driving frequency, using a purely mechanical system for demonstration.^3–5 The instructor then extends the inquiry by asking students to predict what happens to the magnetic system when the driving frequency decreases. Prediction in demonstrations has been proven to increase student learning.^18,19 Last, the experiment is performed. In this way, student learning progresses from what they are very familiar with (swings) to a more advanced concept smoothly.

The solenoid technique uses the invisible alternating current to generate a periodic magnetic force, driving the oscillation of the small compass. One of its challenges is the invisibility of this periodic change in the driving magnetic force, which can make it difficult for students to comprehend. In contrast, our method, which is based on the rotation of a magnet, offers a direct and visible representation of the changing magnetic field (force). This visibility underscores the link between cause and effect for learners. Furthermore, our approach is marked by its simplicity. There is no need for solenoids, computers, or a tone generator app. With just three inexpensive magnets, readily available in most school labs, our method facilitates a quick, cost-effective, and intuitive qualitative demonstration that is accessible even to audiences without a physics background.

However, there are also limitations to the proposed demonstration, with the most significant one being the difficulty of quantitatively measuring the rotation frequency of the large compass. While this measurement can be achieved through video analysis, it is neither timely nor straightforward for a classroom demonstration. Instead, the solenoid technique allows for precise control of the driving frequency, making it a better choice for quantitative experimental investigations.

In summary, we introduce a simple yet effective approach for demonstrating (magnetic) resonance in introductory physics courses. Unlike previous techniques that use alternating current and depend on unseen processes, our approach capitalizes on the rotation of a large compass. This rotation creates visible periodic variation, driving the oscillation of the small compass. Providing a visible representation of the shifting magnetic field can help students better understand the underlying physics of this phenomenon. Moreover, our technique stands out for its simplicity and cost-effectiveness, requiring only three standard magnets often available in school labs.

I would like to express my sincere gratitude to the referees for their constructive suggestions that greatly enhanced this presentation. The Guangdong Office of Philosophy and Social Sciences supported this project under its Education Sciences category with grant number GD24CJY43.

Yajun Wei received his PhD from Uppsala University in Sweden in 2015. Thereafter, he worked as a physicist at Uppsala University and Cambridge University, and as a physics and engineering teacher at Zhuhai No.1 High School in China. He is now an associate professor of physics education research at Guangzhou University, China. runnerwei@qq.com