SCIENCE · INVESTIGATE AND EXPLAIN

Separate a charged cavity from conductor material

A conductor in electrostatic equilibrium has no electric field inside its material: a sustained field would continue driving mobile charge. This statement does not say that every empty cavity inside a conductor is field-free. A charge placed in a cavity can produce a field there while charges on the cavity wall rearrange so that the surrounding conducting material remains at constant potential.

Learning outcome: Compare central charges −2,0,+2 nC at shell total +1 nC, retaining inner/outer totals and all three field regions. Then set shell total to minus the central charge. Explain which regions become field-free and why a charged cavity can still retain a field.

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 central +2 nC and shell total +1 nC, inner charge is −2 nC and outer charge +3 nC. At .5 m the outward field is k×2 nC/.25; at 1.5 m it is zero; at 3 m it is k×3 nC/9. The shell charge still sums to +1 nC.

Open the experiment

Predict

For central +2 nC and isolated shell total −2 nC, the exterior field is:

Your prediction and reason

Experiment

Compare central charges −2,0,+2 nC at shell total +1 nC, retaining inner/outer totals and all three field regions. Then set shell total to minus the central charge. Explain which regions become field-free and why a charged cavity can still retain a field.

Distinguish cavity charge from conductor material

Worked teaching model · synthetic values · Concentric spherical conducting shell inner radius 1 m, outer radius 2 m with a fixed central point charge. Electrostatic equilibrium in vacuum. Evaluate fields at .5, 1.5 and 3 m; no material surface value is sampled. No grounding wire or external field.

Central point charge: 2 nC Isolated shell total charge: 1 nC

Reset keeps your prediction, captures and practice history.

Radial fields in three distinct regions

Unlike graph quantities rescale independently; read units and values, not screen angles. 1: cavity samples (solid).2: conductor interior (dashed).3: exterior samples (dotted). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Radial fields in three distinct regions

cavity samples

radius (m)	outward signed field (N/C)
0.25	287.602
0.5	71.9004
0.75	31.9557

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.

conductor interior

radius (m)	outward signed field (N/C)
1.1	0
1.9	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.

exterior samples

radius (m)	outward signed field (N/C)
2.1	6.11398
2.5	4.31402
3	2.99585

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
Inner shell surface charge	-2	nC
Outer shell surface charge	3	nC
Shell charge sum	1	nC
Cavity field at .5 m outward signed	71.9004	N/C
Conductor material field at 1.5 m	0	N/C
Exterior field at 3 m outward signed	2.99585	N/C
Shell potential relative to infinity	13.4813	V

The material has zero equilibrium field; the charged cavity generally does not.

The inner surface cancels the central charge for any enclosing surface in the conductor. Shell total charge fixes the outer remainder. Spherical symmetry makes these surface distributions uniform and permits point-source exterior formulas. An off-center cavity charge would make the inner distribution nonuniform; do not carry the simple cavity radial formula into that changed geometry. Surface fields are discontinuous and not interpolated across gaps.

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

The material has zero equilibrium field; the charged cavity generally does not.

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 model is a concentric spherical shell with inner radius 1 m, outer radius 2 m, central point charge q and isolated shell total charge Qs. The inner surface carries −q. Conservation of the shell charge therefore puts Qs+q on the outer surface. These are distinct recipient totals; the central point charge is not part of the shell. Spherical symmetry makes the distributions uniform and gives the familiar radial fields: kq/r² in the cavity, zero in the material and k(Qs+q)/r² outside.

Test an alternative before claiming identification

At the two material surfaces the ideal field changes discontinuously; do not join a graph across a surface as if it were a smooth measured transition. The shell potential relative to infinity is k(Qs+q)/(2 m), and is constant throughout its material. If the central charge is moved off-center, the inner distribution is no longer uniform and the simple cavity radial formula fails. External fields, openings, time variation and actual grounding arrangements are additional boundary conditions, not details this ideal model certifies. No real shielding, electrical safety or wiring decision follows from these virtual calculations.

Worked original case

Investigation

Changed-case practice

Try the changed case before feedback

A central −3 nC charge lies inside an isolated shell whose total charge is +5 nC. Find the outer surface charge in nC.

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.

The cavity/surface-charge distinction is additionally checked against University Physics, conductors in electrostatic equilibrium. The symmetric field formulas are supplied algebraic consequences here; a surface-integral proof is not required in this algebra-based course.

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: Distinguish a field null from a zero potential Next: Keep source potential separate from pair energy

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.