Magnetic fields and field lines
Key idea: A compass’s north end aligns with the resultant magnetic field. Outside a bar magnet, field lines run from N to S; inside they return from S to N, forming closed loops.
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Guided steps
- Use the compass’s north end to read the local field direction.
- Follow the force on a north test pole.
- Predict the compass direction and choose the field definition.
- Relate arrows and spacing to field direction and strength.
- Compare crossing directions with the compass’s single settled direction.
- Explain why crossing field lines contradict the compass reading.
- Follow each north-end dot with the next south-end placement.
- Choose the next compass placement and the arrow-direction tool.
- Read the facing poles before comparing the field patterns.
- Choose the arrows and central line pattern in the gap.
- Correct the arrows and sketch the complete unlike-pole pattern.
- Decide whether unequal magnets still give zero field at the midpoint.
- Explain the plotting difficulty and suggest an improvement.
- Sketch all three patterns and compare their labels, arrows and shapes.
- Review local compass directions and the complete field patterns.
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A magnet affects a compass needle even when the two are not touching. The space around a magnet where this happens is its magnetic field. You cannot see a field, but a small compass shows its direction at any point, and field lines turn those directions into a picture. This lesson shows how to find a field’s direction and how to draw the patterns you need.
Magnetic fields and their direction
A magnetic field is a region in which a magnetic pole, or a piece of magnetic material, experiences a force.
The direction of a magnetic field at a point is the direction of the force on a north pole placed there. A small plotting compass shows it: its north-seeking end points in the field direction.
Outside a bar magnet, this makes the field point away from the north pole and towards the south pole. Inside the magnet, the field runs from south to north, so every field line forms a closed loop.
Worked example 1
Why field lines run from north to south
Problem
Use the definition of field direction to explain why field lines outside a bar magnet point from its north pole to its south pole.
Show full solution
Place a north pole near the magnet
Method
Imagine a small north pole placed in the space around the magnet.
Reason
Field direction is defined as the direction of the force on a north pole.
Working
Answer
The test north pole is repelled by the magnet’s N and attracted by its S.
Read off the direction
Method
Both forces push the test pole away from N and towards S.
Reason
The field arrow points along the force on the test north pole.
Working
Answer
Outside the magnet, field lines run from N to S.
Quick check
A compass needle’s north end is a north pole, so it is pushed along the field line too. That is why it points in the field direction.
Check your understanding 1 Predict the needle
A bar magnet lies horizontally with N on the left and S on the right. A plotting compass is placed just beyond S, on the same horizontal axis. Ignore the Earth’s field. Which way does the needle’s north end point, and why?
Show answer
The north end points left, towards the nearby S pole. Field direction is defined by the force on a north test pole, so the field points into S on this side. The compass aligns with the field at its position.
Rules for field lines
Field lines are a model of the field, not threads in space. When you draw them:
- add arrows to show the direction, from N to S outside the magnet;
- draw lines closer together where the field is stronger, near the poles of a bar magnet;
- never let two lines cross.
Check your understanding 2 One point, one direction
Two field lines cross with different tangents at X, where the field is non-zero. How many field directions does the drawing assign at X, and how many directions can a freely turning compass’s north end settle along?
Show answer
The crossing with different tangents assigns two field directions at X. A compass aligns along the one non-zero resultant field there. The conflict explains why field lines cannot cross; it is not resolved by drawing two arrows or blaming the compass.
Try it yourself 1
A diagram with crossing lines
Problem
A student’s field diagram shows two field lines crossing at point X, where the field is not zero. Use what a plotting compass would do at X to explain why the diagram is wrong.
Ask how many ways the compass can point
Use the compass at X to explain the contradictory directions, then state the corrected rule. Work on paper or here, then compare the complete reasoning with the model below. You need not transcribe your paper work.
Hints
Hint 1
what a line shows
At each point, a field line shows the direction a compass would point.
Hint 2
at the crossing
How many directions do two crossing lines give at X?
Show solution step by step
Read the diagram at X
Method
The two lines give two different directions at X.
Reason
Each line shows the field direction along it.
Working
Answer
Crossing lines would make the compass point two ways at once.
Compare with a real compass
Method
A compass at X settles in one direction only.
Reason
The fields of all nearby magnets combine into a single field at X, with one direction.
Working
Answer
There is one field direction at X, so field lines cannot cross. The diagram is wrong.
Quick check
Where the field is non-zero, it has one direction. Crossing field lines would give two directions at the same point.
Plotting a field line with a compass
To plot a field line around a bar magnet:
- Place the magnet on a sheet of paper, draw round it and label N and S. Keep other magnets and iron objects away.
- Put a small plotting compass near one pole. When the needle settles, mark a dot at each end of the needle.
- Move the compass so that its south end is over the dot made by its north end. Mark the new position of the north end.
- Repeat until you reach the other pole or the edge of the paper.
- Join the dots with a smooth curve, and add an arrow in the direction the north end pointed.
- Start again from other points near the poles to plot more lines.
Moving the compass so its south end sits on the last north-end dot makes each step start where the last one finished, so the dots join up into one continuous line. Iron filings sprinkled round a magnet show the shape of the pattern quickly, but they cannot show the direction; only the compass can.
The compass responds to the combined field of the magnet and the Earth. Close to the magnet, the magnet’s field is much stronger and decides the direction. Far from the magnet, the Earth’s field takes over, and the needle simply points north.
Check your understanding 3 Choose the next plotting step
You have marked the north end of a settled plotting compass. Which end should you place over that dot for the next step? Can iron filings alone tell you the field-line arrow direction?
Show answer
Put the compass’s south end over the previous north-end dot, wait for it to settle and mark its new north end. Join the successive dots smoothly and add arrows along the north-end pointing direction. Filings alone show shape, without identifying which way an arrow should point.
You can compare your predictions with the bar magnet view of the magnetism and induction lab.
Fields between two magnets
When two magnets are close, their fields combine. Read the facing poles before drawing anything.
- Unlike poles (N facing S): lines run straight across the gap from N to S. Between flat, close poles the lines are nearly parallel and evenly spaced, so the field there is almost uniform: the same strength and direction everywhere in that region.
- Like poles (N facing N): lines leave both north poles and bend away from each other. No line joins the two poles. For identical aligned magnets and with the Earth’s field and other fields ignored, the two fields at the midpoint are equal and opposite, so they cancel. A compass there is not turned by the magnets; this point is called a neutral point.
- S facing S: the same shape as N facing N, but the arrows point into each south pole.
Check your understanding 4 Set the arrows before sketching
A flat N pole on the left faces a flat S pole on the right across a narrow gap. Choose the arrow direction and describe the central part of the gap.
Show answer
Arrows point right from N into S. For close, flat poles, central lines are nearly straight, parallel and equally spaced; they curve near the edges. The source fields reinforce in the gap rather than cancelling.
Spot the mistake 1
Field between unlike poles
Learner diagram
Two flat poles, N and S, face each other across a narrow gap. A learner draws the field lines in the gap with arrows leaving both poles and meeting in the middle. Explain the error and describe the correct pattern.
Use one direction rule throughout
On paper, correct the arrows and sketch the complete pattern in the gap and around the magnets. Explain your changes on paper or here, then compare the whole sketch and reasoning with the model below. You need not transcribe your drawing.
Show solution step by step
Correct the arrows
Method
Field lines leave a north pole and enter a south pole.
Reason
A north test pole in the gap is pushed away from N and pulled towards S, so the force, and the field, points from N to S.
Working
Answer
Every arrow in the gap points from N across to S. No arrow leaves the south pole.
Describe the pattern
Working
Answer
In the middle of the gap the lines are nearly straight, parallel and evenly spaced, showing an almost uniform field. Near the edges they curve outwards. Outside the pair, complete the pattern with curved lines leaving N and entering S, as in the reference figure above. Label the far poles too; no arrow leaves S and no curves cross. Compare the whole sketch, rather than only the central arrows.
Common mistake
Arrows leaving both poles would need a north test pole to be pushed out of both magnets at once. Lines leave only a north pole.
Check your understanding 5
Two identical bar magnets have their south poles facing, with a neutral point midway between them. The left magnet is replaced by a stronger one, with its south pole in the same position. Does the midpoint remain neutral? Which way does a compass’s north end point there? Ignore the Earth’s field.
Show answer
The midpoint is no longer neutral. The left magnet’s field there points left, towards its south pole; the right magnet’s field points right. The left contribution is now stronger, so they do not cancel. The resultant field points left, and the compass’s north end points left too.
Mind stretcher 1 Very near the poleExtension
Why is it hard to plot a neat field line with a compass placed very close to the pole of a strong magnet?
Work on paper or here, then compare the cause and a useful improvement below.
Show answer
Near a pole the field direction changes quickly from one point to the next, even across the length of the compass needle. A tiny change in the compass position then makes a large change in where it points, so the dots do not join smoothly. A smaller compass and shorter steps help.
Check your understanding 6 Draw the field patterns
Sketch three patterns on paper: one bar magnet, two identical bar magnets with N facing S, and two identical bar magnets with N facing N. Label every pole, add field arrows and show how spacing and shape change. For all three patterns, ignore the Earth’s field and other sources. Compare your complete sketches with the reference figures and criteria below; a typed note is optional.
Show answer
For one bar magnet, draw smooth outside lines leaving N and entering S, closer together near the poles, without crossings; inside they complete the loops from S to N. For N facing S, connect the facing poles with N-to-S arrows and approximately straight, parallel central lines for the narrow gap, curving out at the edges. For N facing N, lines leave both facing poles and bend apart; do not join the two N poles. Mark the midpoint as neutral only under the stated identical-magnet/no-other-field assumptions. Check each pole label, all arrow directions, the near-pole spacing, non-crossing curves and the different gap patterns. Use the figures above for the full shape; the sketches need not trace them exactly.
Common mistakes
- Drawing arrows from S to N outside a magnet. Outside, field lines run from N to S.
- Drawing field lines that cross, or that touch each other.
- Joining like poles with field lines. Lines from two north poles bend away from each other.
- Leaving arrows off field lines, or using iron filings alone to find the direction.
- Thinking a compass points at the centre of the nearest pole. It points along the field line at its own position.
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