Draw the field around an isolated charged conducting sphere
Use radial external lines for an isolated conducting sphere and specify the electrostatic-equilibrium assumptions behind the pattern.
Section P4.1 · Electrical quantities
Cross-referenced to the 2028–2029 0653 section using original teaching from the related single-science courses. A 0653-specific objective-by-objective and Core/Supplement review is in progress. Written practice is self-checked and does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Draw isolated point-charge fields.
- Explain mobile electrons in a conductor.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is special about a conductor in the simple electron model?
What you will learn
- Draw external field patterns for charged conducting spheres.
- Distinguish the conducting surface and interior from the point-source idealisation.
Start lines at the conducting surface
For an isolated positively charged conducting sphere in electrostatic equilibrium, the external field is radial and outward. Draw lines normal to the spherical surface and spread them around it. For a negatively charged sphere, the same external radial geometry has inward arrows ending at the surface.
Represent the object as a finite sphere rather than a point dot. The external pattern resembles that of a central point charge, but the conductor's interior is a different region. Do not draw arrows through its material as if it were an empty continuation of a point-source sketch.
State the model conditions
In electrostatic equilibrium the mobile charges have settled, leaving no electric field inside the conducting material; otherwise its free charges would continue to move. Excess charge lies at the surface in this ideal isolated model. These explanatory conditions support the required simple pattern rather than a claim about every conductor during current flow.
A nearby charge, another conductor or a grounded connection can change the arrangement and surface distribution. The symmetric sketch assumes those influences are absent. Field lines show geometry and direction, not an exact force or charge value determined by how many lines were drawn. A negative test particle's force remains opposite to the local field.
Sources for this lesson
Pause and explain
Where should arrows be drawn for the isolated charged sphere's simple equilibrium pattern?
Worked example
Sketch an isolated negative conducting sphere in electrostatic equilibrium and give the external field direction at its left surface.
Show the worked solution
- Draw a circle for the finite sphere.
- External radial arrows point inward to the negative surface.
- At the left, inward is rightward; the equilibrium conducting interior has no field.
Answer External radial inward arrows; left-side field rightward; no field in the equilibrium conducting interior.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Describe a field sketch for an isolated positive conducting sphere at electrostatic equilibrium.
Give me a hint
Use a finite circle and external lines normal to the surface.
Compare my reasoning
- Draw the conducting sphere boundary.
- Draw radial external lines leaving the surface with outward arrows.
- Keep the equilibrium conducting interior free of field lines.
Radial outward external arrows, normal to the surface; no equilibrium interior field.
Look for these in your work
- Label the positive surface.
- Distinguish inside and outside.
For an isolated negative sphere, state field directions just above and just right of its surface.
Give me a hint
The field points inward at both positions.
Compare my reasoning
- Above the sphere, inward is downward.
- To its right, inward is leftward.
- Both arrows end toward the negative surface.
Above: downward; right: leftward.
Look for these in your work
- Use the position-specific directions.
- Retain inward arrows for the negative source.
A second charged object is brought close to one side of the sphere. Can the original isolated radial sketch be assumed unchanged?
Give me a hint
Check the changed external influences on mobile charge distribution.
Compare my reasoning
- The second object adds an external electric influence.
- The conductor's mobile charges can redistribute.
- The isolated symmetric pattern is no longer guaranteed.
No; the nearby source can alter the surface distribution and resultant external pattern.
Look for these in your work
- Identify the lost isolation assumption.
- Avoid treating the simple sketch as universal.
Common mistakes
- Begin or end external lines at the sphere surface.
- Keep the equilibrium conducting interior distinct.
- A nearby source can invalidate the isolated symmetric model.
What can you explain now?
Are external field arrows outward or inward for a positive isolated conducting sphere?
Compare with the explanation
Outward.
A positive test charge is repelled normally away from its surface.
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Make it stick
Draw charged-sphere fields with correct external arrows and explicit isolation and equilibrium conditions.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.