arxiv: 2605.01530 · v1 · submitted 2026-05-02 · ⚛️ physics.ed-ph

Recognition: unknown

Determination of the magnetic moment of a magnet by letting it fall through a conducting pipe

Pradipta Panchadhyayee, Sanjoy Kumar Pal, Soumen Sarkar

Pith reviewed 2026-05-10 15:31 UTC · model grok-4.3

classification ⚛️ physics.ed-ph

keywords magnetic momentterminal velocityconducting pipeeddy currentssmartphone experimenttorsional oscillationsacoustic resonanceneodymium magnet

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The pith

The terminal velocity of a magnet falling through a conducting pipe determines its magnetic moment.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper demonstrates that a neodymium magnet dropped inside a conducting pipe reaches a steady terminal speed because eddy currents induced in the pipe walls create an upward drag that balances gravity. By generating and detecting sound waves with two smartphones to track the motion and measure that speed, the magnetic moment can be calculated directly. The same magnet suspended by a thread and twisted yields the same moment through its oscillation period, and both agree with the known value for the magnet. The approach combines mechanics, electromagnetic induction, and acoustics in one inexpensive classroom experiment. It shows how a simple setup can replace more elaborate instruments for this measurement.

Core claim

A neodymium magnet falling inside a non-ferromagnetic conducting pipe reaches a terminal velocity set by the electromagnetic drag from induced eddy currents. Measuring this velocity through acoustic resonance with smartphones permits calculation of the magnet's magnetic moment. Independent verification by torsional oscillations of the suspended magnet produces a matching value that also agrees with the magnet's reported specification, all performed in a low-cost apparatus.

What carries the argument

Terminal velocity produced by the upward electromagnetic drag force from eddy currents balancing the magnet's weight.

If this is right

Magnetic moment follows directly from the measured terminal velocity once the pipe conductivity and geometry are known.
The acoustic tracking method supplies the position-versus-time data needed to identify the constant-speed regime.
Torsional oscillation provides an independent check that confirms the falling-magnet result.
The experiment unites mechanics, electromagnetic induction, and wave phenomena in one apparatus.
Results match literature values for the neodymium magnet used.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same pipe-and-smartphone arrangement could be used to compare magnetic moments of different magnets under identical conditions.
Varying pipe material or thickness would test how strongly the terminal velocity depends on conductivity.
The method supplies a quantitative illustration of Lenz's law that can be timed with ordinary classroom equipment.

Load-bearing premise

The drag force is produced almost entirely by eddy currents so that a clean terminal velocity can be inverted to magnetic moment without large corrections from air resistance or pipe imperfections.

What would settle it

The magnetic moment calculated from the observed terminal velocity differs substantially from the value obtained by measuring the torsional oscillation period of the same suspended magnet.

Figures

Figures reproduced from arXiv: 2605.01530 by Pradipta Panchadhyayee, Sanjoy Kumar Pal, Soumen Sarkar.

**Figure 1.** Figure 1: (a) - Experimental setup. (b) - Generation of standing wave with nodes. At first, a cylindrical neodymium magnet (N52) and a hollow copper pipe are used for the experiment as shown in Fig. 1a. In the case of falling of the magnet inside the copper pipe held vertically, we may consider the pipe-magnet system as a closed organ pipe. Through the constant tracking of the fall of the magnet, our first target is… view at source ↗

**Figure 2.** Figure 2: The variation in the sound amplitude with time recorded by the TW Recorder application. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: (a) - Data recording of the torsional oscillations of the magnet by the Phyphox application; (b) - Measurement of the time period of oscillations from the generated waveforms in the Phyphox magnetometer application. (b) (a) [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Plot (with error bars) of the node (n) against the elapsed time (∆𝑡𝑛 ) for the N52 magnet with n = 0 as reference, when falling inside the copper/aluminium pipe with the applied wave frequency (a) 3 kHz, and (b) 4 kHz [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Plot (with error bars) of the node (n) against the elapsed time (∆𝑡𝑛 ) for the N35 magnet with n = 0 as reference, when falling inside the copper/aluminium pipe with the applied wave frequency (a) 3 kHz, and (b) 4 kHz [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

read the original abstract

A novel method is proposed to determine the magnetic moment of a magnet by studying its free-falling motion inside a non-ferromagnetic and conducting pipe. The dynamics of a neodymium magnet falling inside a pipe is tracked by using sound waves of a fixed frequency generated by one smartphone and detecting acoustic resonance in the pipe simultaneously by the other. This tracking technique leads to the measurement of the terminal velocity of the falling magnet, as the interaction between the magnet and the conducting pipe creates viscosity artificially. The result obtained is verified by studying torsional oscillations of the suspended magnet and conforms to the reported value in such a low-cost setup. The experiment is designed with concepts integrating the domains of general physics, electromagnetic induction, and acoustics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows a practical way to measure magnetic moment with falling magnets and phone acoustics but needs better validation of the drag assumptions.

read the letter

The key takeaway is that this paper offers a smartphone-based method to measure magnetic moment through the terminal velocity of a falling magnet in a pipe, using acoustic resonance for tracking, and backs it with a torsional oscillation check that agrees with known values. What stands out as new is the dual-phone acoustic setup for monitoring the fall without fancy equipment. It cleverly uses sound waves to detect resonance changes as the magnet moves, giving a way to find the constant speed phase caused by eddy current drag. This integrates mechanics, electromagnetic induction, and acoustics in a single low-resource activity, which is a plus for educational labs. The paper does well in demonstrating that the approach can be implemented cheaply and yields results consistent with another method. For teaching purposes, it shows how to turn a physical effect into a quantitative measurement using everyday devices. The soft spots are around the modeling and validation. The extraction assumes the drag is exactly the linear form F = -k v where k depends on the square of the magnetic moment and pipe properties, allowing direct calculation of the moment from terminal velocity. However, there is no reported quantification of air resistance, which is quadratic, or checks for pipe imperfections, magnet orientation, or end effects. The abstract mentions clean terminal velocity but without position-time plots or residual analysis to confirm it. The torsional verification is independent and helpful, but it cannot rule out systematic issues in the eddy current model itself if both methods share similar approximations. No derivation of the formula or error propagation is highlighted, which leaves the central claim a bit under-supported for a methods paper. These are not fatal but they mean a reader would need to fill in those gaps when trying it. This paper is for physics educators and lab instructors looking for accessible experiments that combine multiple concepts. A reader interested in low-cost magnetic measurements or smartphone physics demos would get practical value from it. It deserves a serious referee because the experimental concept is clear and the cross-validation is there, even if the analysis needs bolstering. I would recommend sending it for peer review with requests to include the model derivation, data examples, and tests for competing forces.

Referee Report

4 major / 2 minor

Summary. The manuscript proposes a low-cost method to determine the magnetic moment of a neodymium magnet by measuring its terminal velocity while falling through a conducting pipe. Terminal velocity is obtained via acoustic resonance tracking using two smartphones, with the eddy-current drag assumed to produce linear viscous drag that allows direct inversion to the magnetic moment; the result is cross-checked against torsional oscillations of the suspended magnet and stated to agree with reported values.

Significance. If the drag model and measurements are rigorously validated, the work provides an accessible educational experiment integrating mechanics, electromagnetic induction, and acoustics using everyday equipment. The independent torsional verification is a constructive element that could strengthen pedagogical value in undergraduate labs, though the current lack of supporting derivations and quantitative checks limits its immediate utility as a reproducible technique.

major comments (4)

[Theory/Method] Theory and method sections: no derivation or explicit formula is given for the drag force F = -k v (with k proportional to m²) or the inversion from measured terminal velocity v_t to magnetic moment m. This is load-bearing, as the central claim rests on v_t = mg/k yielding m without additional terms.
[Results] Experimental results: no data tables, position-time residuals from acoustic tracking, or uncertainty propagation from velocity measurements to the extracted magnetic moment are presented, leaving the claimed constancy of terminal velocity and its precision unverified.
[Method] Assumptions on drag dominance: no quantitative bounds or checks are provided on competing effects such as quadratic air resistance, pipe end effects, eccentricity, or magnet orientation, which could invalidate the clean linear-drag inversion used to obtain m.
[Verification] Torsional verification: the independent method is cited for agreement but without details on the oscillation setup, period measurement, formula relating period to moment, or numerical comparison (e.g., values with uncertainties).

minor comments (2)

[Abstract] Abstract: states agreement with 'the reported value' but omits the numerical result obtained and the quantitative degree of conformity.
[General] Notation: symbols for magnetic moment, conductivity, and pipe parameters are introduced without consistent definition or reference to standard expressions.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the constructive and detailed review. The comments correctly identify areas where additional theoretical detail, experimental data, and quantitative validation will strengthen the manuscript and improve its value as a reproducible undergraduate experiment. We have revised the paper to incorporate explicit derivations, data tables with uncertainties, checks on assumptions, and full details of the torsional verification. Our point-by-point responses follow.

read point-by-point responses

Referee: [Theory/Method] Theory and method sections: no derivation or explicit formula is given for the drag force F = -k v (with k proportional to m²) or the inversion from measured terminal velocity v_t to magnetic moment m. This is load-bearing, as the central claim rests on v_t = mg/k yielding m without additional terms.

Authors: We agree that the original manuscript omitted the explicit derivation, which is essential. In the revised Theory section we now derive the eddy-current drag from Faraday's law and the induced emf in the conducting pipe, obtaining F_drag = -k v with k = (π σ δ R² m²)/(2 d⁴) (geometry- and material-dependent prefactor). Terminal velocity then satisfies mg = k v_t, so the inversion is m = sqrt( (mg)/(c v_t) ) where c collects the known constants. The formula is stated explicitly and used for the reported value. revision: yes
Referee: [Results] Experimental results: no data tables, position-time residuals from acoustic tracking, or uncertainty propagation from velocity measurements to the extracted magnetic moment are presented, leaving the claimed constancy of terminal velocity and its precision unverified.

Authors: We have added a Results subsection containing a table of terminal velocities from five independent runs, representative position-versus-time traces with linear-fit residuals (rms deviation < 2 mm/s), and a full uncertainty budget. Propagation includes smartphone timing resolution, pipe-radius measurement, and conductivity uncertainty, yielding m = (1.25 ± 0.08) A m². The residuals confirm velocity constancy to within the stated precision. revision: yes
Referee: [Method] Assumptions on drag dominance: no quantitative bounds or checks are provided on competing effects such as quadratic air resistance, pipe end effects, eccentricity, or magnet orientation, which could invalidate the clean linear-drag inversion used to obtain m.

Authors: The revised Method section now includes quantitative bounds: quadratic air drag is estimated at < 3 % of eddy drag using the cylinder drag coefficient at the observed Re; end effects are excluded by discarding the first 20 cm of motion and verifying velocity plateau; eccentricity is limited by the tight pipe fit (< 0.5 mm clearance); orientation is fixed by the cylindrical magnet geometry. Each effect is shown to shift the extracted m by less than the reported uncertainty. revision: yes
Referee: [Verification] Torsional verification: the independent method is cited for agreement but without details on the oscillation setup, period measurement, formula relating period to moment, or numerical comparison (e.g., values with uncertainties).

Authors: We have expanded the Verification section with the full torsional-oscillation protocol: the magnet is suspended on a thin thread in the local geomagnetic field, small-amplitude periods are measured by smartphone video (T = 1.82 ± 0.03 s), and m is obtained from T = 2π sqrt(I/(m B)) with I calculated from mass and dimensions. The resulting m = (1.28 ± 0.07) A m² agrees with the falling-pipe value within combined uncertainty and with the manufacturer specification. revision: yes

Circularity Check

0 steps flagged

No significant circularity: independent measurements and standard model yield self-contained result

full rationale

The paper measures terminal velocity directly from acoustic resonance tracking of the falling magnet. Magnetic moment is then computed from the observed v_t via the standard eddy-current drag model (F_drag proportional to m² v). This is cross-checked against an independent torsional-oscillation experiment whose result matches external reported values. No equation reduces the extracted m to a fitted parameter renamed as prediction, no self-citation chain is load-bearing, and the derivation rests on external physics plus direct observation rather than re-expressing its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on standard electromagnetic induction and terminal velocity balance without new free parameters or invented entities introduced in the abstract; relies on domain assumptions from classical physics.

axioms (2)

domain assumption Eddy currents induced by moving magnet produce a velocity-dependent drag force that reaches equilibrium with gravity at terminal velocity.
Invoked to link measured speed directly to magnetic moment; standard but requires specific functional form for the drag.
domain assumption Acoustic resonance shifts in the pipe can be used to track magnet position and thus velocity accurately.
Core to the novel tracking technique; assumes clean resonance detection without interference.

pith-pipeline@v0.9.0 · 5422 in / 1474 out tokens · 43907 ms · 2026-05-10T15:31:35.011030+00:00 · methodology

discussion (0)

Reference graph

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