SCIENCE · INVESTIGATE AND EXPLAIN

End an electric trajectory at its first boundary event

A uniform electric field gives a passive charge constant force qE. In this fictional model the bead has q=1 nC and mass 10⁻⁸ kg, enters halfway between plates with horizontal velocity and zero vertical velocity, and experiences no gravity. The vertical acceleration is a_y=qE/m=0.1E in SI units. Horizontal velocity stays constant because the ideal field is vertical.

Learning outcome: Compare E=−100,0,+100 N/C at fixed horizontal speed. Then increase speed to 3 m/s and classify the first event again. Retain event times, endpoint and work/energy residual rather than extrapolating all paths to the far edge.

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

For E=100 N/C and vx=2 m/s, a_y=10 m/s². Contact occurs at √.02≈.141421 s before exit at .2 s. At contact x≈.282843 m, y=.1 m and vy≈1.414214 m/s. Work qEΔy=10⁻⁸ J matches the gained vertical kinetic energy.

Open the experiment

Predict

If plate contact occurs before horizontal exit, the valid endpoint is:

Your prediction and reason

Experiment

Compare E=−100,0,+100 N/C at fixed horizontal speed. Then increase speed to 3 m/s and classify the first event again. Retain event times, endpoint and work/energy residual rather than extrapolating all paths to the far edge.

Stop the trajectory at the first plate or exit event

Worked teaching model · synthetic values · Fictional bead q=1 nC, mass=1e−8 kg enters at y=0 with vy=0. Plates at y=±.1 m, length .4 m, uniform field inside and no gravity. A first contact or horizontal exit ends the model; no post-contact or fringe prediction. Virtual only.

Vertical field upward: 100 N/C Initial horizontal speed: 2 m/s

Reset keeps your prediction, captures and practice history.

Trajectory only up to first event

Spatial axes use the same pixels per physical unit, preserving geometry. 1: bounded bead trajectory (solid). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Trajectory only up to first event

bounded bead trajectory

x (m)	y (m)
0	0
0.00707107	0.0000625
0.0141421	0.00025
0.0212132	0.0005625
0.0282843	0.001
0.0353553	0.0015625
0.0424264	0.00225
0.0494975	0.0030625
0.0565685	0.004
0.0636396	0.0050625
0.0707107	0.00625
0.0777817	0.0075625
0.0848528	0.009
0.0919239	0.0105625
0.0989949	0.01225
0.106066	0.0140625
0.113137	0.016
0.120208	0.0180625
0.127279	0.02025
0.13435	0.0225625
0.141421	0.025
0.148492	0.0275625
0.155563	0.03025
0.162635	0.0330625
0.169706	0.036
0.176777	0.0390625
0.183848	0.04225
0.190919	0.0455625
0.19799	0.049
0.205061	0.0525625
0.212132	0.05625
0.219203	0.0600625
0.226274	0.064
0.233345	0.0680625
0.240416	0.07225
0.247487	0.0765625
0.254558	0.081
0.26163	0.0855625
0.268701	0.09025
0.275772	0.0950625
0.282843	0.1

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
Vertical acceleration	10	m/s²
First event time	0.141421	s
First event x	0.282843	m
First event y	0.1	m
First event is contact (includes tie)	1	flag
Horizontal velocity at event	2	m/s
Vertical velocity at event	1.41421	m/s
Kinetic energy gain	1e-8	J
Electric work to event	1e-8	J
Potential difference to event	-10	V

The first plate contact ends the model before any later exit prediction.

Use a_y=qE/m, y=a_y t²/2 and x=v_x t. Compare event times before evaluating endpoints; the zero-field case has no plate-contact event. Work qE Delta y equals the kinetic-energy increase, with Delta V=−E Delta y. Contact is not a continuation through a plate; a simultaneous exit/contact is labeled explicitly by the contact flag.

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

The first plate contact ends the model before any later exit prediction.

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

The plate region has length .4 m and surfaces at y=±.1 m. Horizontal exit time is .4/vx. When E is nonzero, contact time is √(.2/|a_y|), obtained from |y|=|a_y|t²/2. Evaluate the trajectory only up to the earlier event. A calculation that continues past the first plate contact is not an alternative valid prediction: it has left its own physical domain. At zero field there is no plate-contact event in this model.

Test an alternative before claiming identification

The endpoint energy check is independent of the time-root procedure: electric work qEΔy equals the gain in kinetic energy, and ΔV=−EΔy. Reversing E reverses vertical displacement and velocity but leaves work positive for this initially un-deflected positive bead, because the product EΔy stays positive. A negative charge would instead reverse the acceleration at fixed field. Fringe fields, contact forces and motion after exit are absent; no actual charged particle apparatus or electrical experiment is requested.

Worked original case

Investigation

Changed-case practice

Try the changed case before feedback

For E=0 and horizontal speed 2 m/s, find the exit time in seconds.

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: Keep source potential separate from pair energy Next: Reconstruct a uniform field from a voltage survey

Save a science backup or import one

Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.

A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.

Choose a science backup (maximum 36 MB)

Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.

Complete file sets and course backups

A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.

Export scope

The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.

Choose the manifest and all parts together

0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.

Science storage: loading. No account or remote computation is required.