SCIENCE · INVESTIGATE AND EXPLAIN

Use an oriented normal in a signed flux-change account

Magnetic flux through a flat surface in a uniform field is Φ=BAcosθ, with θ measured from the oriented surface normal. Flux is signed; it is not simply field magnitude times an unlabeled area. The normal also fixes a positive boundary circulation by the right-hand rule. Reversing that convention reverses both reported flux and emf signs without changing the physical event.

Learning outcome: Compare normal angles0,60,90,120 degrees and two durations. Retain initial/final signed flux before computing emf. Then on paper hold B=.2 T and rotate one .02 m² turn from aligned to perpendicular: flux changes by−.004 Wb rather than zero.

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

At duration .4 s and θ=60 degrees, linkage change is .06 Wb turn, so emf is −.15 V. At120 degrees the cosine reverses sign and emf is +.15 V. At90 degrees it is zero.

Open the experiment

Predict

Lenz direction opposes:

Your prediction and reason

Experiment

Compare normal angles0,60,90,120 degrees and two durations. Retain initial/final signed flux before computing emf. Then on paper hold B=.2 T and rotate one .02 m² turn from aligned to perpendicular: flux changes by−.004 Wb rather than zero.

Use the surface normal and signed flux change

Worked teaching model · synthetic values · Stationary 30-turn coil area .02 m². Uniform field magnitude rises linearly from .1 to .3 T at fixed direction. Positive circulation follows the right-hand rule from the chosen normal. Mean emf equals constant emf within this linear interval; no current without a specified closed circuit.

Field-change interval: 0.4 s Angle from oriented surface normal: 60 degrees

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Signed flux linkage during the linear field change

Unlike graph quantities rescale independently; read units and values, not screen angles. 1: fixed normal and area (solid). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Signed flux linkage during the linear field change

fixed normal and area

time (s)	flux linkage (Wb turn)
0	0.03
0.01	0.0315
0.02	0.033
0.03	0.0345
0.04	0.036
0.05	0.0375
0.06	0.039
0.07	0.0405
0.08	0.042
0.09	0.0435
0.1	0.045
0.11	0.0465
0.12	0.048
0.13	0.0495
0.14	0.051
0.15	0.0525
0.16	0.054
0.17	0.0555
0.18	0.057
0.19	0.0585
0.2	0.06
0.21	0.0615
0.22	0.063
0.23	0.0645
0.24	0.066
0.25	0.0675
0.26	0.069
0.27	0.0705
0.28	0.072
0.29	0.0735
0.3	0.075
0.31	0.0765
0.32	0.078
0.33	0.0795
0.34	0.081
0.35	0.0825
0.36	0.084
0.37	0.0855
0.38	0.087
0.39	0.0885
0.4	0.09

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
Initial signed flux per turn	0.001	Wb
Final signed flux per turn	0.003	Wb
Flux-linkage change	0.06	Wb turn
Mean signed induced emf	-0.15	V
Induced emf is nonzero	1	flag

Flux uses the component along the oriented area normal; a stronger field can still produce zero flux change at ninety degrees.

Phi=BAcosθ and mean emf=−N DeltaPhi/Delta t, with positive circulation tied to the normal by a right-hand rule. The minus sign opposes the flux change, not necessarily the existing magnetic field. Reversing the chosen normal reverses both reported flux and circulation sign without changing the physical event. An induced emf can exist in an open circuit with no sustained conduction current.

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

Flux uses the component along the oriented area normal; a stronger field can still produce zero flux change at ninety degrees.

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

The stationary coil has30 turns and area .02 m². Field magnitude rises linearly from .1 to .3 T over the selected duration while direction and coil orientation remain fixed. Flux-linkage change is30(.02)(.2)cosθ, and mean emf is its negative divided by duration. Because the change is linear, this average equals the constant emf within the interval. At exactly90 degrees the flux change is exactly zero, not a small residual from a rounded cosine.

Separate physical evidence from a model extension

Lenz direction opposes the change in flux, not always the existing field. A decreasing positive flux produces the opposite emf sign from an increasing positive flux. Rotating a coil or changing its area can also change flux without changing field magnitude. Emf can exist in an open loop even when no sustained conduction current flows; current requires a specified circuit resistance and continuity. These are virtual sign conventions, not a coil-handling procedure.

Worked original case

At duration .4 s and θ=60 degrees, linkage change is .06 Wb turn, so emf is −.15 V. At120 degrees the cosine reverses sign and emf is +.15 V. At90 degrees it is zero.

Investigation

Changed-case practice

Try the changed case before feedback

Use the stated30-turn coil with angle0 and field rise .1→.3 T in .6 s. Find signed emf in V.

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.

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

Your explanation and limitations

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