Magnetic field of a solenoid
Key idea: A solenoid's field is strong and nearly uniform inside, and outside it looks like a bar magnet's. More current, more turns or a soft-iron core make it stronger; reversing the current swaps its poles.
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Guided steps
- Follow the outside return loops and the nearly uniform central field.
- For a coil, fingers follow conventional current and the thumb points to N.
- Follow the left-end anticlockwise model before changing the current direction.
- Find both poles and the internal field direction.
- Sketch the field and explain what happens when current stops.
- Separate current direction from magnitude, winding density and core choice.
- Calculate winding densities and choose how to match the fields.
- Predict direction and strength separately for unchanged current magnitude.
- Compare doubling turns and length with doubling only the turns.
- Check the viewing direction, arrows and quantities kept constant.
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Wind a wire into a long coil, called a solenoid, and the fields of its turns reinforce inside to produce a concentrated field with a north and a south pole, just like a bar magnet. Put a soft iron core inside and you have an electromagnet: a magnet you can switch on and off. This lesson describes the solenoid’s field, how to find its poles and how to make it stronger.
The field of a solenoid
Outside the solenoid, the field has the same shape as the field of a bar magnet: lines leave the north end and curve round to the south end. Inside, the lines run from the south end to the north end, completing the loops.
Each turn of the coil has a circular field around its wire. Inside the coil, the fields of all the turns point the same way and add up. So the field inside is strong, and in the middle of a long solenoid the lines are straight, parallel and evenly spaced: the field there is uniform. Near the ends the lines spread out and the field weakens.
Finding the poles
Use the right-hand grip rule, adapted for a coil:
- curl the fingers of your right hand round the solenoid in the direction of the conventional current in the turns;
- your thumb points along the inside of the solenoid towards its north pole.
A quick check: look at one end of the solenoid. If the current goes anticlockwise round that end, it is a north pole; if it goes clockwise, it is a south pole.
Worked example 1
Which end is north?
Problem
Viewed from its left end, the conventional current in a solenoid goes anticlockwise round the turns. Is the left end a north or a south pole?
Show full solution
Curl the fingers with the current
Method
Curl your right-hand fingers anticlockwise, as seen from the left end.
Reason
The fingers follow the conventional current round the turns.
Working
Answer
Your thumb points out of the left end, towards you.
Read the pole
Method
The thumb points to the north pole.
Reason
Inside the solenoid the field runs towards the north end, where the lines come out.
Working
Answer
The left end is a north pole, and the right end is a south pole.
Quick check
The end-view check agrees: anticlockwise current seen from an end makes that end north.
Check your understanding 1 Set the pole labels
Viewed from the left end of a long air-core solenoid, the conventional current is clockwise. Choose both poles and the internal field direction before sketching.
Show answer
The left end is S and the right end is N. The internal field points right from S to N. Outside, lines return from the right N end to the left S end. The end-view current and pole labels must agree with the right-hand grip rule.
Check your understanding 2
Viewed from the left end of a long air-core solenoid, the conventional current is clockwise. Sketch its field, label the poles and add arrows inside and outside. Are the pole labels still valid after the current is switched off?
Draw the field on paper, then compare the full pattern with the reference figure and criteria. Give the separate switch-off conclusion on paper or here; a typed transcript of the drawing is optional.
Show answer
The left end is S and the right end is N. Inside, draw straight, parallel, evenly spaced lines with arrows pointing right, towards N. Outside, draw curved lines from the right end back to the left end, completing closed loops, with lines spreading near the ends. After switching off, the air-core coil produces no magnetic field, so it no longer has these magnetic poles.
Changing the field
Reversing the current reverses the direction of the field, so the poles swap ends. The strength is unchanged if the size of the current is unchanged.
The field becomes stronger if you:
- increase the current, because each turn then produces a stronger field;
- increase the number of turns per unit length, by winding more turns onto the same length of coil, because more turns add their fields in the same space;
- add a soft iron core, because the coil’s field magnetises the iron, and the iron’s own field adds to the coil’s field.
Soft iron is used for the core, not steel, because it loses its magnetism when the current is switched off. That is what lets an electromagnet release whatever it is holding.
You can change the current and the turns and watch the poles in the magnetism and induction lab.
Guided practice 1
Two coils compared
Problem
Coil A has 100 turns wound over a length of 10 cm. Coil B has 100 turns spread over 20 cm. Both carry the same current and have no core. Treat them as long solenoids and compare their central fields, ignoring end effects. Which coil has the stronger field inside it? Give one way to make the weaker coil match the stronger one without changing the current.
Compare winding density, then choose a matching change
Hints
Hint 1
what matters
It is not the total number of turns that matters, but how closely they are packed.
Hint 2
turns per centimetre
Work out the turns per centimetre for each coil.
Show solution step by step
Compare the turns per unit length
Method
Work out how closely each coil is wound.
Reason
The field inside depends on the turns per unit length and the current.
Working
Answer
A: 100 ÷ 10 cm = 10 turns per cm. B: 100 ÷ 20 cm = 5 turns per cm. Coil A has the stronger field.
Strengthen coil B
Method
Wind 200 turns over B’s same 20 cm length.
Reason
Doubling B’s turns to 200 over the same 20 cm gives 10 turns per cm, like A, at the same current. Adding soft iron would strengthen B by an amount that depends on the core and setup, so it may not exactly match A.
Working
Answer
With 200 turns over 20 cm, B matches A’s central field in the stated long-solenoid model. Alternatively, rewinding B’s 100 turns over 10 cm gives the same winding density, if it remains a long solenoid.
Quick check
“More turns” means more turns on the same length. Making a coil longer with its turns equally spread does not strengthen the field inside it.
Check your understanding 3 Predict both effects of reversal
A long air-core solenoid’s current is reversed without changing its magnitude. At the same central point, what happens to the field direction and strength?
Show answer
The field reverses and the pole labels swap. Its strength at the same central point stays the same because the current magnitude and solenoid geometry are unchanged.
Check your understanding 4 More turns, longer coil
A long air-core solenoid is replaced by one with twice as many turns spread over twice the length, at the same current. A learner predicts a stronger central field because there are more turns. Explain what the learner missed. Include what would change if the turns doubled while the length stayed the same. Work on paper or here, then compare both cases below; the note is optional.
Show answer
When both turns and length double, turns per unit length stay the same. At the same current and with no core, the central field stays approximately the same in the long-solenoid model. If only the turns double at the same length, the winding density increases and the central field strengthens. Check that both comparisons state what is held fixed; total turns alone do not settle field strength. The field is nearly uniform centrally, not at the ends or everywhere outside.
Common mistakes
- Using electron flow in the grip rule. Use conventional current.
- Pointing the thumb along the current. For a solenoid, the fingers follow the current and the thumb points to the north pole.
- Saying the field is uniform everywhere. It is uniform only in the middle of a long solenoid; near the ends it spreads out.
- Saying “more turns” without keeping the length the same.
- Choosing a steel core for an electromagnet. It would stay magnetised when the current is switched off.
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Syllabus and review details
- SEC G3 Physics 2027 · 2027
Content Structure, PDF page 9; Subject Content, PDF pages 10–28
Last reviewed: