SCIENCE · INVESTIGATE AND EXPLAIN

Test a magnetic source geometry after removing a probe baseline

A magnetic-field reading depends on source geometry and sensor response. For the long straight vacuum wire approximation, magnitude B=μ0I/(2πr), and the field circles the wire according to the right-hand rule for conventional current. At radii .05 and .10 m the physical fields differ by a factor of two, but a common additive sensor offset can hide that ratio.

Learning outcome: Change only offset and compare raw ratios with difference-based current. Freeze the third-radius prediction. Separately compare an ideal solenoid with n doubled at fixed I and a loop with R doubled at fixed NI: predict factors two and one half.

Starting recap

Use a right-handed coordinate system, oriented surface normal, signed charge/current and declared energy boundary. Separate an entry force from a trajectory, emf from current, and rms from signed average.

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Try

For I=3 A and offset1 µT, near reading is13 µT and far7 µT. The difference recovers12 µT physical near field, offset1 µT and current3 A. At .15 m the withheld indication is5 µT.

Open the experiment

Predict

Two fitted wire-field readings establish:

Your prediction and reason

Experiment

Change only offset and compare raw ratios with difference-based current. Freeze the third-radius prediction. Separately compare an ideal solenoid with n doubled at fixed I and a loop with R doubled at fixed NI: predict factors two and one half.

Infer a long-wire current separately from probe baseline

Worked teaching model · synthetic values · Vacuum long-straight-wire approximation, mu0=4pi×10⁻⁷ T m/A. Exact radial distances.05,.10,.15 m, same signed azimuthal component. A common additive sensor offset affects all readings. No nearby return wire, finite length or ferromagnetic material.

Long straight wire current: 3 A Field instrument offset: 1 µT

Reset keeps your prediction, captures and practice history.

Same-component long-wire field with sensor baseline

Unlike graph quantities rescale independently; read units and values, not screen angles. 1: one-over-radius plus offset (solid). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Same-component long-wire field with sensor baseline

one-over-radius plus offset

radial distance (m)	indicated azimuthal field (µT)
0.05	13
0.05375	12.1628
0.0575	11.4348
0.06125	10.7959
0.065	10.2308
0.06875	9.72727
0.0725	9.27586
0.07625	8.86885
0.08	8.5
0.08375	8.16418
0.0875	7.85714
0.09125	7.57534
0.095	7.31579
0.09875	7.07595
0.1025	6.85366
0.10625	6.64706
0.11	6.45455
0.11375	6.27473
0.1175	6.10638
0.12125	5.94845
0.125	5.8
0.12875	5.66019
0.1325	5.5283
0.13625	5.40367
0.14	5.28571
0.14375	5.17391
0.1475	5.0678
0.15125	4.96694
0.155	4.87097
0.15875	4.77953
0.1625	4.69231
0.16625	4.60902
0.17	4.52941
0.17375	4.45324
0.1775	4.38028
0.18125	4.31034
0.185	4.24324
0.18875	4.17881
0.1925	4.11688
0.19625	4.05732
0.2	4

At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.

Calculated quantities under the declared measurement model
Quantity	Value	Unit
Near field indication at .05 m	13	µT
Far field indication at .10 m	7	µT
Recovered near physical field	12	µT
Recovered field offset	1	µT
Inferred wire current	3	A
Withheld .15 m field indication	5	µT

A common field offset disappears from differences but distorts a raw one-over-distance ratio.

For a long straight vacuum wire B=mu0 I/(2pi r), and direction follows a right-hand circulation around conventional current. Doubling r halves the physical field. Two readings identify current and offset only within this geometry; a withheld third radius tests that hypothesis. Finite wires, nearby return paths, ferromagnetic material and a tilted sensor can change the interpretation.

Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.

A common field offset disappears from differences but distorts a raw one-over-distance ratio.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Define vectors, source and system boundary

Derive the quantitative comparison

Let near and far indications be R1=F+o and R2=F/2+o, in the same signed azimuthal component. Then F=2(R1−R2), o=R1−F and I follows from the known near radius. At .15 m the predicted physical field is F/3, providing a withheld geometry test. Two readings fit two parameters only inside the assumed model; they do not prove the source is an infinite straight wire.

Separate physical evidence from a model extension

A circular loop and a long solenoid have different spatial laws. Their supplied ideal center relations are Bloop=μ0NI/(2R) and Bsolenoid≈μ0nI away from ends. Neither supports replacing a long-wire radius by an arbitrary distance in the same formula. Nearby return paths, finite length, tilted probe axes and ferromagnetic material can change observations. Permanent magnets arise from microscopic magnetic moments; their field lines form closed patterns rather than beginning and ending on isolated magnetic charges. No real coil or high-field test is requested.

Worked original case

For I=3 A and offset1 µT, near reading is13 µT and far7 µT. The difference recovers12 µT physical near field, offset1 µT and current3 A. At .15 m the withheld indication is5 µT.

Investigation

Changed-case practice

Try the changed case before feedback

Near/far indications at r and2r are10 and6 µT with common offset. Find physical near field in µT.

Numerical result in the requested units

This practice is public and unsaved. A matching number does not verify understanding. Retain your explanation, assumptions and changed-case evidence in the separate course workspace.

Sources and evidence boundary

Original prose and numerical cases checked 30 October 2026 against the relevant primary explanation. All records and diagrams are virtual. No real coil, powered wire, high-field exposure, motor, transformer, mains connection or inductor switching is requested. Retain first predictions, contrasting recipes and independent criterion review; public agreement is not practical certification or demonstrated mastery.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Which independent observation could reject this model rather than merely refit its parameters?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

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