Compare zero torque with stable and unstable alignment
A loop normal is oriented by the right-hand convention around conventional current. Its magnetic moment is μ=NIA normal_vector, not an arrow lying in the loop plane. For angle θ between that normal and a uniform field, torque magnitude is NIABsinθ. Confusing a plane angle with a normal angle exchanges sine and cosine and can reverse which orientation is called maximum.
Learning outcome: Compare0,60,90,180 degrees at fixed current. Retain torque and potential separately. Perturb each zero-torque state by a small angle and use the potential change to classify stability.
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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For20 turns, area .01 m², current2 A and field .02 T, μ=.4 A m² and μB=.008 J. At60 degrees torque magnitude .004√3≈.0069282 N m and U=−.004 J. Moving quasistatically from aligned to60 degrees increases the effective orientation potential by .004 J.
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Anti-alignment has zero torque but is:
Experiment
Compare0,60,90,180 degrees at fixed current. Retain torque and potential separately. Perturb each zero-torque state by a small angle and use the potential change to classify stability.
Compare zero torque with stable alignment
Worked teaching model · synthetic values · Ideal 20-turn loop area .01 m², uniform B=.02 T. Current is maintained, magnetic moment magnitude NIA. Angle is from oriented loop normal to field. Mechanical orientation potential U=−mu B cos(theta) under this fixed-current convention; no motor construction.
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Orientation potential with fixed maintained current
Unlike graph quantities rescale independently; read units and values, not screen angles. 1: minus mu B cosine (solid). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Orientation potential with fixed maintained current
minus mu B cosine
| normal-field angle (degrees) | mechanical orientation potential (J) |
|---|---|
| 0 | -0.008 |
| 4.5 | -0.00797534 |
| 9 | -0.00790151 |
| 13.5 | -0.00777896 |
| 18 | -0.00760845 |
| 22.5 | -0.00739104 |
| 27 | -0.00712805 |
| 31.5 | -0.00682112 |
| 36 | -0.00647214 |
| 40.5 | -0.00608325 |
| 45 | -0.00565685 |
| 49.5 | -0.00519558 |
| 54 | -0.00470228 |
| 58.5 | -0.00417999 |
| 63 | -0.00363192 |
| 67.5 | -0.00306147 |
| 72 | -0.00247214 |
| 76.5 | -0.00186756 |
| 81 | -0.00125148 |
| 85.5 | -0.000627673 |
| 90 | 0 |
| 94.5 | 0.000627673 |
| 99 | 0.00125148 |
| 103.5 | 0.00186756 |
| 108 | 0.00247214 |
| 112.5 | 0.00306147 |
| 117 | 0.00363192 |
| 121.5 | 0.00417999 |
| 126 | 0.00470228 |
| 130.5 | 0.00519558 |
| 135 | 0.00565685 |
| 139.5 | 0.00608325 |
| 144 | 0.00647214 |
| 148.5 | 0.00682112 |
| 153 | 0.00712805 |
| 157.5 | 0.00739104 |
| 162 | 0.00760845 |
| 166.5 | 0.00777896 |
| 171 | 0.00790151 |
| 175.5 | 0.00797534 |
| 180 | 0.008 |
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.
| Quantity | Value | Unit |
|---|---|---|
| Magnetic moment magnitude | 0.4 | A m² |
| Torque magnitude | 0.0069282 | N m |
| Mechanical orientation potential | -0.004 | J |
| Potential relative to aligned state | 0.004 | J |
| Equilibrium code: 1 aligned stable, -1 anti-aligned unstable, 0 other | 0 | code |
Both aligned and anti-aligned orientations have zero torque, but only alignment is a potential minimum.
The normal follows the right-hand current convention; theta is not measured from the plane of the loop. Torque magnitude NIABsinθ has its maximum at 90 degrees. The effective mechanical orientation potential −mu dot B describes this maintained-current convention; it is not a claim that an isolated circuit has no source-energy exchange. A small deviation from anti-alignment lowers this potential and grows rather than restoring.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
Both aligned and anti-aligned orientations have zero torque, but only alignment is a potential minimum.
The normal follows the right-hand current convention; theta is not measured from the plane of the loop. Torque magnitude NIABsinθ has its maximum at 90 degrees. The effective mechanical orientation potential −mu dot B describes this maintained-current convention; it is not a claim that an isolated circuit has no source-energy exchange. A small deviation from anti-alignment lowers this potential and grows rather than restoring.
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