SCIENCE · INVESTIGATE AND EXPLAIN

Locate the energy source of a motional emf

A rod moving through a magnetic field can separate charge because its carriers experience magnetic force. Here the rod is .3 m long, moves right through .4 T into the page and increases a rectangular loop area. Positive charges are pushed upward along the rod by v cross B. The induced circulation opposes the increasing inward flux and produces magnetic drag on the moving rod.

Learning outcome: Compare two speeds at fixed load and two loads at fixed speed. Retain the external maintaining force and all three power forms. Explain what equation would be added if the external agent stopped maintaining speed.

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 v=1 m/s and R=3 Ω, emf=.12 V, current=.04 A and drag=.0048 N. Mechanical power .0048 W equals resistor power (.04)²×3=.0048 W. Doubling speed at unchanged R quadruples each power.

Open the experiment

Predict

In the maintained-speed rod model, resistor heat is supplied by:

Your prediction and reason

Experiment

Compare two speeds at fixed load and two loads at fixed speed. Retain the external maintaining force and all three power forms. Explain what equation would be added if the external agent stopped maintaining speed.

Identify the mechanical source of motional electrical power

Worked teaching model · synthetic values · Ideal rod length .3 m moves along +x on rails, B=.4 T into page. Loop area grows; quasisteady resistance, negligible self-inductance/friction/contact resistance. External agent maintains speed. No physical rail/magnet/generator assembly.

Maintained rod speed: 1 m/s Total resistive load: 3 Ω

Reset keeps your prediction, captures and practice history.

Required mechanical power with fixed resistance

Unlike graph quantities rescale independently; read units and values, not screen angles. 1: BL squared times speed squared over R (solid). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Required mechanical power with fixed resistance

BL squared times speed squared over R

maintained rod speed (m/s)	mechanical input power (W)
0.5	0.0012
0.5375	0.00138675
0.575	0.001587
0.6125	0.00180075
0.65	0.002028
0.6875	0.00226875
0.725	0.002523
0.7625	0.00279075
0.8	0.003072
0.8375	0.00336675
0.875	0.003675
0.9125	0.00399675
0.95	0.004332
0.9875	0.00468075
1.025	0.005043
1.0625	0.00541875
1.1	0.005808
1.1375	0.00621075
1.175	0.006627
1.2125	0.00705675
1.25	0.0075
1.2875	0.00795675
1.325	0.008427
1.3625	0.00891075
1.4	0.009408
1.4375	0.00991875
1.475	0.010443
1.5125	0.0109807
1.55	0.011532
1.5875	0.0120967
1.625	0.012675
1.6625	0.0132668
1.7	0.013872
1.7375	0.0144907
1.775	0.015123
1.8125	0.0157688
1.85	0.016428
1.8875	0.0171007
1.925	0.017787
1.9625	0.0184867
2	0.0192

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
Motional emf magnitude	0.12	V
Loop current magnitude	0.04	A
Magnetic drag magnitude	0.0048	N
External maintaining force magnitude	0.0048	N
Mechanical input power	0.0048	W
Resistive heat power	0.0048	W
Electrical transfer power	0.0048	W
Power residual	-8.67362e-19	W

The maintaining agent supplies the heat; the magnetic field is not a free energy source.

With field into the page and motion +x, v cross B separates positive charge upward on the moving rod. Increasing inward flux induces a current whose field opposes that increase; the rod magnetic force opposes motion. Emf=BLv, current=emf/R and drag=ILB give Fv=Iemf=I²R. A larger resistance reduces current and drag at fixed speed; speed is imposed by the external agent, not solved as free acceleration.

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

The maintaining agent supplies the heat; the magnetic field is not a free energy source.

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

For the stipulated quasisteady resistive loop, emf=BLv, current=emf/R and drag magnitude=ILB. An external agent maintains the chosen speed, so its force balances drag. Mechanical input power Fv equals Iemf and equals resistor heat rate I²R. This closes the energy account: the magnetic field is not a free energy supply, and the maintained speed is an imposed condition rather than a solved free-motion trajectory.

Separate physical evidence from a model extension

Increasing resistance reduces current and drag at fixed speed; increasing speed raises both emf and current and raises power quadratically. An open loop can still have a separated-charge emf but would not sustain this resistive current. Self-inductance, contact resistance, friction, finite field boundaries and acceleration would need additional terms. No physical rails, energized load or generator assembly is requested.

Worked original case

At v=1 m/s and R=3 Ω, emf=.12 V, current=.04 A and drag=.0048 N. Mechanical power .0048 W equals resistor power (.04)²×3=.0048 W. Doubling speed at unchanged R quadruples each power.

Investigation

Changed-case practice

Try the changed case before feedback

For the statedB=.4 T,L=.3 m, use speed2 m/s andR=4 Ω. Find mechanical input power in W.

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

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