Compare central and external solenoid field strength
Explain the approximately uniform strong central region of a long coil and retain the end and external-field limits.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Trace internal and external solenoid lines.
- Explain field magnitude and direction.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which way does the central internal field point in a right-N solenoid?
What you will learn
- Explain the approximately uniform strong central region of a long coil and retain the end and external-field limits.
- Use the long-solenoid central approximation while keeping non-uniform ends, external fields and drawing limits explicit.
A long solenoid has a useful central approximation
For a sufficiently long, regularly wound solenoid, the central internal field is relatively strong and approximately uniform. Representative lines there are roughly parallel and similarly spaced under a common drawing convention. Uniform means approximately the same strength and direction through that stated central region.
Near the ends, field lines spread and the central approximation becomes less accurate. Outside, the field curves and is generally weaker away from the ends; it is not universally zero. A short coil or added magnetic core can produce a different detailed field distribution.
Interpret drawings within their convention
Compare line spacing only with common scale, conditions and representative-line convention. A drawing with more arbitrarily selected lines cannot establish a measured strength ratio. A graph or diagram label uniform must identify the region where the approximation is intended.
A compass can indicate direction, but it is not a direct calibrated strength meter. A weak external contribution may be combined with Earth’s field or other sources. Therefore a nearly unchanged compass direction outside does not establish that the solenoid produces exactly zero field there.
Sources for this lesson
Pause and explain
Does the central uniform approximation prove the external field is zero?
Worked example
A long-solenoid diagram has parallel equally spaced lines in its central interior and spreading lines near its ends. Interpret the regions.
Show the worked solution
- Central matched spacing suggests approximate uniformity.
- End spreading shows the central approximation changing.
- The outside field is not thereby proven zero.
Answer Approximately uniform central field; end and external regions are non-uniform and need separate interpretation.
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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 central, end and external regions of a sufficiently long solenoid field.
Give me a hint
Keep the central approximation separate from the rest.
Compare my reasoning
- Central interior is relatively strong and approximately uniform.
- End-region lines spread and the approximation changes.
- External field curves and is generally weaker away from the ends.
Strong approximately uniform centre; non-uniform ends and curved non-zero external field.
Look for these in your work
- Identify all regions.
- Retain the long-solenoid condition.
Two central diagrams use different scales and arbitrary line counts. Can their spacing establish an exact strength ratio?
Give me a hint
A valid comparison requires a common representation and calibration.
Compare my reasoning
- Their spatial scales differ.
- Their representative-line choices also differ.
- No exact strength ratio is established.
No calibrated strength ratio follows from those drawings.
Look for these in your work
- Name both representation changes.
- Avoid treating line count as measurement.
A compass outside a solenoid points nearly north with current on. A report claims no solenoid field exists outside. Critique it.
Give me a hint
The observed direction belongs to the resultant field.
Compare my reasoning
- The external solenoid contribution may be weak.
- Earth and other fields can dominate direction.
- A nearly unchanged needle direction does not prove exact zero contribution.
The zero-field conclusion is unsupported; account for background and measurement sensitivity.
Look for these in your work
- Separate observation from claim.
- Retain external field and background contributions.
Common mistakes
- Uniformity is a stated region approximation.
- Outside does not mean zero.
- Line count is not a calibrated strength ratio.
What can you explain now?
What does approximately uniform field mean in the stated central region?
Compare with the explanation
Approximately unchanged strength and direction
The approximation concerns both properties within the specified region, not every point in space.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Use the long-solenoid central approximation while keeping non-uniform ends, external fields and drawing limits explicit.
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.