Disconnect ground before removing the inducing charge
You will be able to: Track grounding, induced charge and the order of disconnection.
How can an object acquire charge without touching the charged rod?
Hold a positive charge near a metal sphere and connect the sphere to ground. Electrons can enter from Earth. Disconnect ground first, then remove the external charge: the excess electrons remain on the isolated sphere.
A useful starting point: Connected conductors share potential, not equal charge →
Words and symbols before equations
- Ground
- A large charge reservoir assigned V = 0; it can provide or absorb charge.
- Induction
- Charging through redistribution and a temporary connection without touching the external charge.
- Isolation
- Removing conductive paths so the object’s total charge is fixed.
- Source distance D
- Distance from sphere center to the external point charge; D must exceed R.
What this picture assumes
A grounded sphere of radius R = 0.10 m with a point source at D > R. Stage 0: grounded with source; 1: disconnect ground first; 2: then remove source; 3: alternative, remove source while still grounded. Stages are settled states, not an animation. Total induced charge is exact; the surface distribution is not drawn.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Stage 0: Source present; ground connected. Sphere net charge = -2 nC. Diagram is schematic; induced density is not uniform while the source is near.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
A grounded sphere must have V = 0, not necessarily Q = 0. For a point charge q a distance D from the center of a grounded sphere of radius R, the exact induced total is Q_sphere = −qR/D. Its nonuniform density is not shown by the total-charge ledger.
The image-charge method gives that total: a mathematical charge −qR/D at R²/D from the center reproduces the exterior potential with a zero-potential spherical boundary. The image is a calculation device, not a real charge hidden in the metal.
After disconnecting ground while the source stays nearby, the sphere retains that net charge. Removing the source afterward redistributes it uniformly. If the source is removed while ground remains connected, charge flows back and the sphere ends neutral in the absence of other fields.
A worked example, step by step
A +6 nC point charge is held D = 0.30 m from the center of a grounded sphere with R = 0.10 m. What remains after disconnecting ground and then removing the source?
- Check D > R so the source lies outside.
- While grounded, Q_sphere = −6(0.10/0.30) = −2 nC.
- Disconnecting ground prevents further net transfer, locking in −2 nC.
- Removing the source leaves −2 nC spread uniformly on the isolated sphere.
Ground fixes potential, not charge. Reversing the disconnection order can change the final result.
What happens with a negative inducing charge?
Compare with an explanation
Electrons leave through ground; disconnecting first leaves the sphere positively charged.
Predict. Change one thing. Explain.
Use the stage control to compare grounded-near-source, ground disconnected, source removed after isolation, and source removed while still grounded. Track which steps allow charge exchange.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Stage 0: Source present; ground connected. Sphere net charge = -2 nC. Diagram is schematic; induced density is not uniform while the source is near.
A grounded sphere of radius R = 0.10 m with a point source at D > R. Stage 0: grounded with source; 1: disconnect ground first; 2: then remove source; 3: alternative, remove source while still grounded. Stages are settled states, not an animation. Total induced charge is exact; the surface distribution is not drawn.
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 questionExplain two sequences: (A) disconnect ground then remove a positive source; (B) remove the source then disconnect ground. Compare final sphere charges.
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Compare with the answer and four-point rubric
- 1 point: With the source present and ground attached, negative charge enters the sphere.
- 1 point: In A, disconnecting first fixes this negative total.
- 1 point: Removing the source in A changes distribution but not total charge.
- 1 point: In B, ground remains available as the source is removed, so the sphere returns to neutral before disconnection.
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 1Does ground create electrons?
No; it supplies or receives existing charge as a large reservoir.
RECALL 2Is an image charge physical?
No. It reproduces the exterior boundary-value solution mathematically.
RECALL 3What matters in induction charging?
The external source and the order in which ground and source are removed.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Disconnect ground before removing the inducing charge
- Ground connection: V = 0 by the chosen reference.
- Point source outside grounded sphere: Q_induced = −qR/D.
- After isolation, net conductor charge is conserved.
Remember: Ground fixes potential, not charge. Reversing the disconnection order can change the final result.
Conditions: A grounded sphere of radius R = 0.10 m with a point source at D > R. Stage 0: grounded with source; 1: disconnect ground first; 2: then remove source; 3: alternative, remove source while still grounded. Stages are settled states, not an animation. Total induced charge is exact; the surface distribution is not drawn.
Refresh Kid · AP Physics C: Electricity and Magnetism Unit 3 (official Unit 10) · Objectives 10.2.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 10.2, objectives 10.2.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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