SCIENCE · INVESTIGATE AND EXPLAIN

Distinguish one segment force from whole-loop torque

A current-carrying segment in a uniform magnetic field experiences F=I L_vector cross B, where L_vector follows conventional current. Here the segment lies in the xy plane, has length .2 m and makes angle θ from +x toward +y. The magnetic field is .05 T along +x. Only the y component of the segment contributes, giving Fz=−I(.2)(.05)sinθ.

Learning outcome: Compare 0,30,90,180 degrees at fixed current. Retain signed z force rather than only magnitude. Sketch a rectangular closed loop and identify two forces that cancel as vectors but can still produce a torque.

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 θ=90 degrees and I=4 A, Fz=−4(.2)(.05)=−.04 N. At θ=30 degrees the same current gives −.02 N. At 0 or180 degrees it is exactly zero despite nonzero current and field.

Open the experiment

Predict

A closed current loop in a spatially uniform magnetic field can have:

Your prediction and reason

Experiment

Compare 0,30,90,180 degrees at fixed current. Retain signed z force rather than only magnitude. Sketch a rectangular closed loop and identify two forces that cancel as vectors but can still produce a torque.

Resolve the force on one current-carrying segment

Worked teaching model · synthetic values · Straight segment length .2 m in xy plane; uniform B=.05 T along +x. Current follows the segment orientation. Only this segment force is calculated; a closed loop in uniform field has separate forces whose vector sum is zero.

Segment angle from +x toward +y: 90 degrees Conventional current: 4 A

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One segment force versus orientation

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

Equivalent numerical coordinates for One segment force versus orientation

I L cross B

segment angle (degrees)	signed z force (N)
0	0
4.5	-0.00313836
9	-0.00625738
13.5	-0.00933781
18	-0.0123607
22.5	-0.0153073
27	-0.0181596
31.5	-0.0208999
36	-0.0235114
40.5	-0.0259779
45	-0.0282843
49.5	-0.0304162
54	-0.0323607
58.5	-0.0341056
63	-0.0356403
67.5	-0.0369552
72	-0.0380423
76.5	-0.0388948
81	-0.0395075
85.5	-0.0398767
90	-0.04
94.5	-0.0398767
99	-0.0395075
103.5	-0.0388948
108	-0.0380423
112.5	-0.0369552
117	-0.0356403
121.5	-0.0341056
126	-0.0323607
130.5	-0.0304162
135	-0.0282843
139.5	-0.0259779
144	-0.0235114
148.5	-0.0208999
153	-0.0181596
157.5	-0.0153073
162	-0.0123607
166.5	-0.00933781
171	-0.00625738
175.5	-0.00313836
180	0

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
Segment force x	0	N
Segment force y	0	N
Segment force z	-0.04	N
Segment force magnitude	0.04	N
Conventional charge crossing per second	4	C/s

The transverse segment component controls force; parallel and antiparallel orientations give exact zero.

I L cross B uses conventional-current direction, not electron drift direction. Here L=(Lcosθ,Lsinθ,0) and B=(B,0,0), so Fz=−ILBsinθ. Reversing current reverses force. In a closed loop inside a spatially uniform field, opposite segments cancel net force while separated forces can still make a torque; one-segment force is not the whole-loop resultant.

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

The transverse segment component controls force; parallel and antiparallel orientations give exact zero.

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

Parallel and antiparallel orientations give exact zero force. At θ=90 degrees the magnitude is maximal and direction is −z for positive conventional current. Reversing current reverses the force. Electron drift is opposite conventional current in an ordinary metal, but substituting electron direction for the defined current vector without also handling charge sign would reverse the answer incorrectly.

Separate physical evidence from a model extension

This is the force on one selected segment, not automatically the force on a complete circuit. In a closed loop within a spatially uniform field, the vector sum of all segment forces is zero. Nevertheless, forces applied at separated positions can form a couple and produce torque. A nonuniform field can also give a net force, but that requires a different source model. The line drawing and current values are virtual geometry, not wire placement or energized apparatus instructions.

Worked original case

At θ=90 degrees and I=4 A, Fz=−4(.2)(.05)=−.04 N. At θ=30 degrees the same current gives −.02 N. At 0 or180 degrees it is exactly zero despite nonzero current and field.

Investigation

Changed-case practice

Try the changed case before feedback

For the stated .2 m segment and .05 T field, use θ=30 degrees and I=6 A. Find signed Fz in N.

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

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Previous: Resolve curvature without inventing a neutral gyroperiod Next: Compare zero torque with stable and unstable alignment

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