SCIENCE · INVESTIGATE AND EXPLAIN

Resolve a field before assigning a probe force

A field represents the source configuration at an observation point. For each point source, draw the displacement from source to observation point and use E=kQ r_vector/r³. Its magnitude is k|Q|/r², but signed components are essential when fields are not collinear. Add components from different sources before calculating the magnitude of the resultant; adding magnitudes discards cancellation.

Learning outcome: Compare second-source charges −4, 0 and +4 nC and retain each source component separately. Then hold sources fixed and change only the probe sign, including zero. Explain which arrows change and why a field-line picture is not a particle track.

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.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

At a=−2 nC, field components are k×10⁻⁹(5,2)/(5√5), about (4.01936,1.60774) N/C. A +1 nC probe has force components about (4.01936,1.60774) nN; a −1 nC probe reverses both.

Open the experiment

Predict

Changing only a passive probe from +q to −q changes:

Your prediction and reason

Experiment

Compare second-source charges −4, 0 and +4 nC and retain each source component separately. Then hold sources fixed and change only the probe sign, including zero. Explain which arrows change and why a field-line picture is not a particle track.

Resolve a field independently of the probe charge

Worked teaching model · synthetic values · Sources +3 nC at (−1,0) m and selected charge at (1,0) m. Evaluate at (0,2) m. Probe is passive and does not alter sources. A zero probe still has a well-defined ambient field.

Second source charge: -2 nC Probe charge: 1 nC

Reset keeps your prediction, captures and practice history.

Original source geometry, not field-line trajectories

Spatial axes use the same pixels per physical unit, preserving geometry. 1: +3 nC source to observation point (solid).2: selected source to observation point (dashed). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Original source geometry, not field-line trajectories

+3 nC source to observation point

x (m)	y (m)
-1	0
0	2

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.

selected source to observation point

x (m)	y (m)
1	0
0	2

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.

Field component addition at the common observation point

Unlike graph quantities rescale independently; read units and values, not screen angles. 1: Ex (open markers).2: Ey (filled markers). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Field component addition at the common observation point

Ex

source index	component (N/C)
1	2.41161
2	1.60774

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.

Ey

source index	component (N/C)
1	4.82323
2	-3.21548

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
Electric field x component	4.01936	N/C
Electric field y component	1.60774	N/C
Electric field magnitude	4.32898	N/C
Probe force x component	4.01936e-9	N
Probe force y component	1.60774e-9	N
Field direction from +x	21.8014	degrees

Add field vectors from sources before multiplying by the probe charge.

Each source is sqrt(5) m away, with signed direction determined by charge. Components use displacement divided by distance cubed. A negative probe reverses force relative to field; a zero probe feels no electric force but does not erase the field. Field arrows represent local force direction on a positive passive probe, not a guaranteed particle path.

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

Add field vectors from sources before multiplying by the probe charge.

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

Here sources lie at (−1,0) and (1,0) m, and the observation point is (0,2) m. Both distances are √5 m. The +3 nC source contributes components proportional to (3,6), while the second charge a in nC contributes (−a,2a). Thus E=k×10⁻⁹(3−a,6+2a)/(5√5). The common geometric scale permits a direct vector check against the original equal-scale diagram.

Test an alternative before claiming identification

Only after the field is found do we use F=q_probe E. A negative probe reverses force relative to E; a zero-charge probe has zero electric force while the ambient field remains defined. The passive-probe assumption excludes source motion and polarization caused by the probe. A local field arrow indicates acceleration direction for a positive charge under electric force alone, not necessarily its velocity or the complete trajectory of a particle that already has velocity.

Worked original case

At a=−2 nC, field components are k×10⁻⁹(5,2)/(5√5), about (4.01936,1.60774) N/C. A +1 nC probe has force components about (4.01936,1.60774) nN; a −1 nC probe reverses both.

Investigation

Changed-case practice

Try the changed case before feedback

Keep the source geometry but set the right source to +3 nC. Give the resultant x component in N/C.

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: Test an inverse-square force after removing a baseline Next: Distinguish a field null from a zero potential

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