Fields inside and around conductors
You will be able to: Explain electrostatic equilibrium and distinguish conducting and insulating spheres.
Why must the field vanish inside a conductor at rest?
If a steady electric field persisted inside conducting metal, its mobile charges would keep moving. At electrostatic equilibrium, they have redistributed so the net field within the conducting material is zero.
A useful starting point: Read and combine electric field vectors →
Words and symbols before equations
- Electrostatic equilibrium
- No continuing macroscopic charge redistribution.
- Excess charge
- Net charge beyond the material’s neutral balance.
- Surface normal
- Direction perpendicular to a surface.
- Spherical symmetry
- Charge distribution is the same under rotations about the center.
What this picture assumes
Isolated solid conducting sphere, radius 0.20 m and charge +2 nC, in electrostatic equilibrium. Interior field zero; exterior is spherically symmetric. At the ideal surface, report distinct inside/outside limits. Insulator interior is treated qualitatively in Learn.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- At r=0.4 m, E=112.5 N/C outward. Radius is measured from the center.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Excess charge on an isolated solid conductor resides on its surface. The field just outside is perpendicular to that surface; a tangential component would drive further movement. This statement concerns electrostatics, not current flowing in a resistive wire.
For an isolated sphere with spherically symmetric charge, the external field equals that of a point charge Q at its center. Inside the conducting material E=0. At the ideal charged surface the field jumps; do not average inside and outside formulas.
Insulators can retain excess charge within their volume as well as on surfaces, depending on how charge was deposited. Their internal field need not be zero. AP-level internal-insulator analysis here is qualitative; no formula for a uniformly charged insulating sphere is required.
A worked example, step by step
An isolated conducting sphere of radius 0.20 m carries +2 nC. Find E at r=0.10 m and r=0.40 m.
- The 0.10 m point is inside the solid conductor: E=0.
- The 0.40 m point is outside; use distance from the center.
- E=kQ/r²=9×10⁹(2×10⁻⁹)/0.40²=112.5 N/C.
- The external field points radially outward.
E=0 inside conducting material in electrostatic equilibrium does not mean the conductor has zero potential or zero surface charge.
Must an insulator’s field vanish inside?
Compare with an explanation
No. Bound or deposited charges can sustain an internal field.
Predict. Change one thing. Explain.
Move the probe from inside to outside a radius-0.20 m conductor. The exact surface is labeled as a boundary with distinct limiting values; it is not treated as an ordinary interior point.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
At r=0.4 m, E=112.5 N/C outward. Radius is measured from the center.
Isolated solid conducting sphere, radius 0.20 m and charge +2 nC, in electrostatic equilibrium. Interior field zero; exterior is spherically symmetric. At the ideal surface, report distinct inside/outside limits. Insulator interior is treated qualitatively in Learn.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant charge, field 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 conducting sphere with radius R has charge +Q in isolation. (a) State E at R/2. (b) Give E at 2R. (c) Describe surface-field direction. (d) Explain why an insulator need not share the interior result.
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Compare with the answer and four-point rubric
- 1 point: E=0 in the conducting material.
- 1 point: E=kQ/(4R²), outward.
- 1 point: Perpendicular to the surface.
- 1 point: Insulating charge cannot freely redistribute to cancel all interior field.
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 1Why zero E inside equilibrium metal?
A persistent field would drive mobile charge motion.
RECALL 2Where is excess charge on a solid conductor?
On its surface in electrostatic equilibrium.
RECALL 3What symmetry permits the external point-charge model?
An isolated spherically symmetric charge distribution.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Fields inside and around conductors
- Solid conductor in electrostatic equilibrium: E_inside=0.
- Isolated symmetric sphere, outside: E=kQ/r² radially.
- External surface field is perpendicular to the conductor.
Remember: E=0 inside conducting material in electrostatic equilibrium does not mean the conductor has zero potential or zero surface charge.
Conditions: Isolated solid conducting sphere, radius 0.20 m and charge +2 nC, in electrostatic equilibrium. Interior field zero; exterior is spherically symmetric. At the ideal surface, report distinct inside/outside limits. Insulator interior is treated qualitatively in Learn.
Refresh Kid · AP Physics 2 Unit 2 (official Unit 10) · Objectives 10.3.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 10.3, objectives 10.3.B. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Refresh Kid calls this the second AP Physics 2 unit; College Board numbers it Unit 10; the first unit in this course is official Unit 9. 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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