Charge mobility changes the field inside matter
You will be able to: Compare an isolated conducting sphere with a uniformly charged insulating sphere.
Why is the static field inside metal zero but not necessarily inside plastic?
In metal, mobile charges keep moving if an internal electric field pushes them. Once the charges settle into electrostatic equilibrium, the field inside the conducting material must be zero. Fixed charges in an insulator do not have the same freedom.
A useful starting point: Read a field map as a vector sum at each point →
Words and symbols before equations
- Electrostatic equilibrium
- Charges have settled; there is no sustained redistribution driven by a static field.
- Excess charge
- Net charge beyond the balanced positive and negative charges in neutral matter.
- Surface normal
- A direction perpendicular to the surface.
- Uniform volume charge
- An ideal insulator with the same charge per unit volume throughout; not a rule for all insulators.
What this picture assumes
Compare a solid isolated conductor in electrostatic equilibrium with a uniform volume-charged solid insulator, at identical Q and R, without external fields. The conducting-surface value at r = R is the exterior limit. Insulators in general need not have uniform charge.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- At r = 0.5 m, R = 1 m: conductor 0 N/C; uniform insulator 9 N/C. At the conducting surface use the exterior limit.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
In electrostatic equilibrium, E = 0 within conducting material. Otherwise mobile carriers would still feel a force and move. Excess charge lies on surfaces. A hollow cavity containing other charges requires separate care; this lesson models a solid isolated sphere.
The field immediately outside a conductor is perpendicular to its surface; a tangential component would move surface charge. For an isolated conducting sphere with no external fields, spherical symmetry gives E = kQ/r² outside.
For a uniformly charged solid insulating sphere of radius R, the interior field is kQr/R³, rising from zero at the center. Charge in a general insulator need not be uniform. We derive the ideal sphere result later using enclosed charge and Gauss’s law.
| Property | Conductor | Insulator |
|---|---|---|
| Charge mobility | Mobile carriers redistribute | Excess charge can remain localized |
| Field within material | Zero in electrostatic equilibrium | Can be nonzero |
| Charge distribution | Excess charge on surfaces | Specified by preparation; not necessarily uniform |
A worked example, step by step
Compare two spheres with Q = +1 nC and R = 1 m: one conducting, one uniformly charged insulating. Find E at r = 0.5 m and r = 2 m.
- Inside conducting material at r = 0.5 m, E = 0.
- For the uniform insulator, E = kQr/R³ = 9(0.5) = 4.5 N/C outward.
- Outside either sphere at r = 2 m, E = kQ/r² = 9/4 = 2.25 N/C outward.
- The same total charge gives the same external spherical field, but different interior fields.
Electrostatic equilibrium is essential for E = 0 in a conductor. An insulator is not automatically uniformly charged.
Could a neutral conductor have separated surface charges?
Compare with an explanation
Yes. An external field can induce a redistribution even when its net charge is zero.
Predict. Change one thing. Explain.
Move the radial probe from inside to outside. Compare both spheres at the same Q and R. The conductor has a jump at its charged surface; the displayed value there is the exterior limit.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
At r = 0.5 m, R = 1 m: conductor 0 N/C; uniform insulator 9 N/C. At the conducting surface use the exterior limit.
Compare a solid isolated conductor in electrostatic equilibrium with a uniform volume-charged solid insulator, at identical Q and R, without external fields. The conducting-surface value at r = R is the exterior limit. Insulators in general need not have uniform charge.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant charge, vector superposition, electric field, flux or symmetry 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 uniformly charged insulating sphere has Q = +2 nC and R = 1 m. Calculate E at r = 0, 0.5 and 2 m, then state which interior results change if it is conducting.
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Compare with the answer and four-point rubric
- 1 point: At the center E = 0 by symmetry.
- 1 point: At 0.5 m, E = 18(0.5) = 9 N/C outward.
- 1 point: At 2 m, E = 18/4 = 4.5 N/C outward.
- 1 point: A conductor has E = 0 at both interior points; the outside value is unchanged.
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 1Where is excess static charge on a conductor?
On its surfaces.
RECALL 2Why no tangential surface field?
It would drive charge along the surface.
RECALL 3Must an insulator have zero interior field?
No. Its charges can remain fixed in a distribution producing nonzero E.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Charge mobility changes the field inside matter
- Conducting material at electrostatic equilibrium: E = 0.
- Isolated spherical exterior: E = kQ/r².
- Uniform insulating interior: E = kQr/R³.
Remember: Electrostatic equilibrium is essential for E = 0 in a conductor. An insulator is not automatically uniformly charged.
Conditions: Compare a solid isolated conductor in electrostatic equilibrium with a uniform volume-charged solid insulator, at identical Q and R, without external fields. The conducting-surface value at r = R is the exterior limit. Insulators in general need not have uniform charge.
Refresh Kid · AP Physics C: Electricity and Magnetism Unit 1 (official Unit 8) · Objectives 8.3.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 8.3, objectives 8.3.B. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. This is E&M Unit 1: Electric Charges, Fields, and Gauss’s Law, numbered Unit 8 in the official combined Physics C sequence. Topics 8.1–8.6 retain their official identifiers. Quantitative force examples use at most four point charges. Field integrals use the specified rods, ring, arc and infinite wire; Gauss-law field calculations use spherical, cylindrical or planar symmetry. Optional projected 3D views clarify area normals and geometry; camera rotation never changes the physics. 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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