SCIENCE · INVESTIGATE AND EXPLAIN

Test an inverse-square force after removing a baseline

Coulomb force for two stationary point charges has magnitude k|qQ|/r² and acts along the line joining them. Like signs repel and unlike signs attract. The two reciprocal forces have equal magnitude and act on different recipients; changing one mass would change its acceleration, not break the force-pair relation. This lesson studies force readings rather than asserting that an instrument directly reveals the ideal force.

Learning outcome: Compare offsets −1, 0 and +1 µN at fixed source charge, retaining raw ratios and recovered force. Then change source magnitude. Freeze a third-distance prediction before revealing it; name a non-electrical calibration alternative if it disagrees.

Starting recap

Use signed charge, common coordinate axes, SI units, vector components and algebraic ratios. Separate a source field from probe force and a fitted parameter from independently tested evidence.

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Try

With source 3 nC, probe 2 nC and r=.1 m, physical force is 5.39253107538 µN. Offset .5 µN gives near 5.89253107538 and far 1.848132768845 µN. Their difference recovers 5.39253107538 µN; the third prediction is 1.09917011949 µN.

Open the experiment

Predict

Why can the two raw force readings fail a four-to-one ratio?

Your prediction and reason

Experiment

Compare offsets −1, 0 and +1 µN at fixed source charge, retaining raw ratios and recovered force. Then change source magnitude. Freeze a third-distance prediction before revealing it; name a non-electrical calibration alternative if it disagrees.

Separate inverse-square force from a sensor baseline

Worked teaching model · synthetic values · Two positive point charges, source selected and probe 2 nC. Synthetic force at exact separations .1 and .2 m, common additive force offset. Vacuum k=8.9875517923e9 N m²/C². Finite sizes and force backreaction are neglected.

Source charge magnitude: 3 nC Force sensor offset: 0.5 µN

Reset keeps your prediction, captures and practice history.

Force indications versus separation

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

Equivalent numerical coordinates for Force indications versus separation

inverse square plus baseline

separation (m)	indicated force (µN)
0.1	5.89253
0.1075	5.16633
0.115	4.57753
0.1225	4.09352
0.13	3.69085
0.1375	3.35225
0.145	3.06482
0.1525	2.81874
0.16	2.60646
0.1675	2.42204
0.175	2.26083
0.1825	2.11907
0.19	1.99378
0.1975	1.88248
0.205	1.78317
0.2125	1.69419
0.22	1.61416
0.2275	1.54191
0.235	1.47647
0.2425	1.417
0.25	1.3628
0.2575	1.31328
0.265	1.26789
0.2725	1.22621
0.28	1.18782
0.2875	1.1524
0.295	1.11965
0.3025	1.08931
0.31	1.06114
0.3175	1.03494
0.325	1.01054
0.3325	0.987764
0.34	0.966482
0.3475	0.946563
0.355	0.927894
0.3625	0.910371
0.37	0.893903
0.3775	0.878407
0.385	0.863807
0.3925	0.850037
0.4	0.837033

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 force indication	5.89253	µN
Far force indication	1.84813	µN
Recovered near physical force	5.39253	µN
Recovered force offset	0.5	µN
Recovered source charge	3e-9	C
Third-point predicted indication at .3 m	1.09917	µN

The force difference removes the additive baseline before an inverse-square ratio is tested.

At twice the separation the physical force is one quarter, but the indicated readings need not have ratio four. Fnear=(4/3)(Rnear−Rfar), then offset=Rnear−Fnear. Two readings fit two unknowns under the chosen law; a withheld third separation tests that law, not merely its fitted parameters. Signed indication can be negative with a negative baseline even though the repulsive force magnitude remains positive.

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

The force difference removes the additive baseline before an inverse-square ratio is tested.

Observation to attach to a capture

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

Understand

Define the source and measurement boundary

Derive the quantitative comparison

Write the near indication R₁=F+o and the indication at twice the distance R₂=F/4+o. Subtraction cancels the common additive offset: F=(4/3)(R₁−R₂). Then o=R₁−F. A raw ratio R₁/R₂ need not equal four even when the physical force obeys the inverse-square model. Conversely, two readings fit the two parameters under that model and do not by themselves prove the exponent.

Test an alternative before claiming identification

Predict a third reading at three times the near distance: R₃=F/9+o. Disagreement can challenge the inverse-square point-source assumptions, the constant baseline, the distance scale, or source stability. It does not uniquely identify which assumption failed. Keep charge in coulombs and separation in metres before calculating; converting a micro-newton readout to newtons is a unit conversion, while estimating an offset is an evidence-based calibration step. Finite conducting objects may redistribute charge at close separation, outside the fixed point-charge model.

Worked original case

Investigation

Changed-case practice

Try the changed case before feedback

At distances r and 2r, indications are 7 and 2.5 µN with one unknown common offset. Find the near physical force in µN.

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 teaching, numerical cases and diagrams checked 30 October 2026 against the relevant primary textbook explanation. No textbook exercise, image or passage is reproduced. These are bounded synthetic records, not observed apparatus. No charging, wiring, capacitor handling, medical application or safety certification is requested. Preserve first predictions, contrasting settings and critiques in the course evidence workspace; public feedback is not independent mastery or performed laboratory time.

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.

Previous: Account for charge across an object and its reservoir Next: Resolve a field before assigning a probe force

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