A cavity is different from the surrounding metal
You will be able to: Use Gauss’s law to distinguish the metal, an empty cavity and a cavity containing charge.
Does a metal shell make every enclosed field zero?
A sealed metal shell can shield an empty cavity from an external static field. Put a charged bead inside that cavity, however, and the bead still creates a field there. The metal rearranges without making the bead disappear.
A useful starting point: A metal sphere has flat potential inside →
Words and symbols before equations
- Cavity
- A nonmetal region enclosed by a conducting shell.
- Inner surface charge
- Charge on the metal boundary facing the cavity.
- Shell net charge S
- Total charge belonging to the metal, not including the bead.
- Gaussian surface
- An imaginary closed surface used to apply electric flux and enclosed charge.
What this picture assumes
Concentric spherical shell with a centered point charge, no contact and no external fields. Charge ledger is exact for the totals; radii in the schematic are not physical scales. A charged cavity generally has nonzero field.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Inner -3 nC + outer 2 nC = shell total -1 nC. Charged cavity: generally nonzero field.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Draw a Gaussian surface in the metal around the cavity. E = 0 on that surface, so its enclosed charge is zero. A bead q inside requires total inner surface charge −q, independent of the bead’s position.
If the isolated shell itself has net charge S, conservation gives outer surface charge S + q. The bead and inner induced charge cancel in the metal-side charge ledger, not at every point in the cavity.
An empty closed cavity has zero electrostatic field in the absence of internal charges. With an internal charge its field generally is not zero. The drawing uses a centered bead and concentric spherical surfaces, where induced densities are uniform; an off-center bead would make the inner density nonuniform.
A worked example, step by step
A +3 nC bead sits inside an isolated shell whose total metal charge is −1 nC. Find the charges on its inner and outer surfaces.
- The Gaussian surface in metal encloses q + Q_inner = 0.
- Thus Q_inner = −3 nC.
- The shell ledger is Q_inner + Q_outer = S = −1 nC.
- Q_outer = +2 nC. The field in metal vanishes; the cavity field does not.
Zero field in metal does not mean zero field in a charged cavity.
If the bead is moved off center, does total inner charge change?
Compare with an explanation
No. Its total remains −q, although its spatial distribution changes.
Predict. Change one thing. Explain.
Change bead charge while holding shell charge fixed. Watch the inner and outer ledgers preserve the shell total. Set q = 0 to compare an empty cavity.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Inner -3 nC + outer 2 nC = shell total -1 nC. Charged cavity: generally nonzero field.
Concentric spherical shell with a centered point charge, no contact and no external fields. Charge ledger is exact for the totals; radii in the schematic are not physical scales. A charged cavity generally has nonzero field.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant conductor equilibrium, charge conservation, capacitance or energy relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA shell has net charge +5 nC and encloses a −2 nC bead without contact. Find both surface charges and explain what changes if the bead moves off center.
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Compare with the answer and four-point rubric
- 1 point: Q_inner = +2 nC to cancel enclosed bead charge in a metal Gaussian surface.
- 1 point: Q_outer = +3 nC so the shell sum stays +5 nC.
- 1 point: The metal remains at E = 0 and constant V.
- 1 point: Moving the bead changes inner density, not its total charge.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What does shielding exclude here?
External static fields from an empty closed cavity.
RECALL 2Can charge exist on an inner surface?
Yes, induced by a charge inside a cavity.
RECALL 3What is conserved for an isolated shell?
The sum of its inner and outer surface charges.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
A cavity is different from the surrounding metal
- Q_inner = −q_cavity.
- Q_outer = S + q_cavity for an isolated shell.
- E_metal = 0 at electrostatic equilibrium.
Remember: Zero field in metal does not mean zero field in a charged cavity.
Conditions: Concentric spherical shell with a centered point charge, no contact and no external fields. Charge ledger is exact for the totals; radii in the schematic are not physical scales. A charged cavity generally has nonzero field.
Refresh Kid · AP Physics C: Electricity and Magnetism Unit 3 (official Unit 10) · Objectives 10.1.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 10.1, objectives 10.1.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. This is E&M Unit 3: Conductors and Capacitors, numbered Unit 10 in the official combined Physics C sequence. Topics 10.1–10.4 retain their official identifiers. Models state the electrostatic conditions, geometry approximations and whether charge or voltage stays fixed. Capacitor geometries include parallel plates, concentric spheres and long coaxial cylinders. Dielectric comparisons assume a fully filling ideal linear material. The optional 3D plate view uses explicitly different gap and lateral scales to show the small separation. Checked with the Fall 2026 clarifications. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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