Magnetism and electromagnetism · Investigation
Magnetic fields
The space around a magnet is not empty. A compass needle finds a direction at every point in it, and joining those directions up is the whole of what a field line is.
Start here
Sprinkle iron filings on the paper and a pattern appears.
A bar magnet sits under a sheet of paper. Scatter iron filings on top, tap the sheet once, and they arrange themselves into curved lines that loop from one end of the magnet round to the other. Nobody moved them into place.
Where did the lines come from?
The field was there before the filings were. Each filing is a scrap of iron, so sitting in the field turns it into a small magnet, and a small magnet turns until it lies along the field — the same thing a compass needle does. Thousands of them do it at once and join up end to end, and the chains they make are the pattern you see. Sweep them off and the field is exactly as it was.
A magnetic field is the region around a magnet where another magnet, or a piece of iron, steel, nickel or cobalt, would feel a force. It is there whether or not anything is in it to feel it, and it fills space in three dimensions — the filings only show you one flat slice of it.
We draw the field with field lines. A line shows the direction a compass needle's north-seeking end would point if you put it at that spot, and the rule is that lines run out of a north pole and into a south pole on the outside of a magnet. Where the lines are crowded together the field is strong; where they spread apart it is weak. Field lines never cross, because a compass at any one point can only point one way.
Plotting a field means doing exactly that, by hand: put a small compass down, mark the direction it settles to, move it along, mark again, and join up the marks. That is the measurement. The lines themselves are a drawing — useful, agreed on by everybody, and not something you would find if you went looking with a microscope.
At the bench · a plotting compass on a field map
Put the compass down and read it.
Change a control to begin
Bearings are measured clockwise from the top of the page.
Commit first. Two bar magnets are laid end to end with their north poles facing each other, a few centimetres apart. A compass is put down exactly half way between them. What does the needle do?
On the paper
Where the compass goes
The needle points
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Field strength here
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Lines near the compass
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The figure
Four rules that let you draw any field
Every field map in physics obeys these four, and every one of them comes straight from what a plotting compass does.
Outside the magnet, every line leaves the north pole and arrives at the south pole. The arrow is the way a compass points.
Crowded lines mean a strong field. Spread-out lines mean a weak one. That is why lines bunch at the poles.
Lines never cross. A compass at a crossing point would have to face two ways at once, and it cannot.
A line is nothing more than a row of compass readings joined up. The compass is the measurement; the line is the drawing.
Key fact
A magnetic field is the region where a magnet or a magnetic material would feel a force, and it is there whether or not anything is in it. Field lines show which way a compass needle points; outside a magnet they run from north pole to south pole, they are crowded where the field is strong, and they never cross.
Think again
“The field is only where the lines are drawn. In between the lines there is nothing.”
The field is everywhere around the magnet, at full strength, in the gaps as much as on the lines. How many lines get drawn is a decision made by whoever is drawing: draw eight and the map looks sparse, draw eighty and it looks dense, and the magnet has not changed. What the spacing carries is a comparison — this part of the map is stronger than that part — not a count of anything real. Put your compass down between two drawn lines and it still swings to a definite direction, because there was a direction there all along.
“The filings make the field.”
Reverse it. The field was there before the filings arrived and stays after you sweep them off. Each filing is a small piece of iron, so being in the field turns it into a tiny magnet, and a tiny magnet in a field turns until it lies along the direction of the field — exactly what a compass needle does, only there are thousands of them and they are free to touch. They line up end to end and the chains they make are what you see. The filings are the detector, not the cause.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Read the map
On a field map of one bar magnet, the lines near the ends are packed close together and the lines out at the sides are far apart. What does that tell you?
Rung 2 · Apply the rule
A student draws a field map in which two lines meet and cross at a point. Why must the drawing be wrong?
Rung 3 · Explain
Explain how you would plot the field around a bar magnet using a plotting compass and a pencil, and say what each pencil mark actually records.
Rung 4 · Take it somewhere new
Two bar magnets are laid end to end with their north poles facing each other, and iron filings are scattered over them. There is a small bare patch on the paper between the two magnets where no filings settle. Explain what is happening there, and say what a compass placed on that patch would do.
Key note
The field is the region around a magnet where a magnet or a magnetic material would feel a force, and it exists whether or not anything is there to feel it. You plot it with a small compass: the needle settles along the field at that point, and joining those directions up gives a field line. Outside the magnet the lines run out of the north pole and into the south. Where they crowd, the field is strong; where they spread, it is weak; and they never cross, because a compass cannot point two ways at once.
Going further
Put two north poles facing each other and somewhere between them is a point where the two fields cancel exactly. A compass there has nothing to turn it and will sit wherever you leave it. Iron filings show the same thing as a bare patch on the paper with lines curving away from it on both sides. It is called a neutral point, and it is worth noticing because it is a place where the field really is zero — which is a different claim from the field being weak, and one of very few places in physics where a quantity is exactly nothing rather than merely small.
The field lines drawn here stop at the ends of the magnet, but they do not really stop: inside the magnet they carry on from the south pole back round to the north, so every line is a closed loop with no beginning and no end. That is a genuine difference from an electric field, whose lines start on positive charges and finish on negative ones. It is the same fact as poles always coming in pairs, seen from another angle — you cannot have a loose end of a loop.
Before this lesson
Connects to
At GCSE this becomes
- Magnetic flux density measured in tesla, the field round a current-carrying wire and a solenoid, and field maps used to work out the force on a conductor.
Where to next
Ask Mr Badmus AI
Stuck on which way the arrows go on a field line?
The bench is a teaching model. Each bar magnet is treated as a pair of point poles at its two ends, which is the standard way of constructing a field map by hand and gives the right shape everywhere except very close to the metal, where a real magnet's field is set by the whole body rather than by its ends. The Earth's own field is left out, so the readings show only what the magnets on the paper do; a real plotting compass adds the Earth's field to them and points somewhere between. Strength is given as a relative figure with the strongest spot the compass can be put on this map set to 100, and no value in tesla is given because that unit is beyond this stage. The arrows drawn across the paper are clamped to a shortest and a longest length, so the crowded regions and the empty ones are both readable rather than drawn to scale. Bearings are clockwise from the top of the page and are rounded to the nearest degree.
Lesson content © MrBadmusAI.