Magnets & Fields of Currents
The Electric Field & Potential topic described the space around a charge as an electric field: the charge changes the space around it, and a second charge placed there feels a force from the field. Magnets work the same way. Bring a compass towards a bar magnet and the needle swings round before anything touches it; an iron nail is pulled towards the magnet across a gap. The magnet has changed the space around it, and the changed space is called a magnetic field (磁场). This topic studies magnetic fields and the forces they exert. This first page asks where the fields come from and what shape they have. It starts with magnets, their poles and their field lines, and with the Earth's field, which is what a compass responds to. Then it turns to the discovery that an electric current makes a magnetic field too, and to the rule that gives the field's direction around a straight wire, a loop and a long coil.
No question in the four papers has tested this page on its own: the topic's questions so far ask about the strength of the field and the forces it exerts, which start on the next page. Its ideas are a step in two Electromagnetic Induction items, though: January 2026, Q33 needs the field of a long straight wire to weaken with distance, and March 2026, Q45 needs the field of a bar magnet passing through a coil. So the page is short. What it must leave you with are two pictures, the field lines of a magnet and of a current, and one rule for their direction, the right-hand grip rule.
Magnetic poles
Roll a bar magnet in iron filings and lift it out. The filings cling thickly to the two ends and hardly at all to the middle. The two regions where the magnet's effect is strongest are its poles (磁极). Hang the magnet from a thread so that it can turn freely, and it settles along a north–south line, always with the same end towards the north. That end is called the north-seeking pole, or N pole, and the other end the S pole. A compass needle is a small magnet that can turn in the same way, and the end that points north is its N pole.
Bring the ends of two magnets together and you find the same rule as for charges: like poles repel and unlike poles attract. There is one difference, though. A positive charge can sit on its own, but a magnetic pole never does. Cut a bar magnet in half across its middle and you do not get an N pole in one hand and an S pole in the other. Each half is a complete magnet with an N pole and an S pole, and new poles appear at the cut. However many times you cut, every piece has two poles. No one has ever found a single N or S pole on its own.
The field and its field lines
Like an electric field, a magnetic field is there whether or not anything is placed in it, and it acts on what is placed in it: on magnets, on iron and, as later sections show, on electric currents. To describe it you need its direction at each point. The electric field took its direction from the force on a positive test charge. The magnetic field takes its direction from a small compass. Put the compass at a point and let it settle: the way its N pole points is the direction of the magnetic field at that point. Put another way, the field pushes an N pole along its direction and an S pole the opposite way, so the needle turns until it lies along the field.
The field also has a strength, written B. The papers call it the magnetic induction intensity and also the magnetic flux density; both names translate 磁感应强度, and both mean the same B. The next page defines B and measures it. This page needs only its direction, and where it is stronger or weaker.
Field lines are drawn exactly as on the Field Lines & Field Patterns page. Start at a point, move a short step the way a compass's N pole points there, and repeat. The steps join into a smooth curve, a magnetic field line, whose tangent at every point gives the direction of the field. The rules for reading the lines carry over too. Where the lines crowd together, the field is strong; where they spread apart, it is weak. And two lines never cross, because at a crossing a compass would have to point two ways at once.
Figure 1 shows the lines of a bar magnet. Outside the magnet they leave the N pole, spread out and curve round to enter the S pole, and they are crowded together near the poles, which is where the filings cling. They do not stop at the S pole. Inside the magnet they carry on, from the S pole back to the N pole, so each line is a closed loop. This is the main difference from electric field lines, which begin on positive charges and end on negative ones. Magnetic lines have nowhere to begin or end, because there are no single poles; it is the fact about the cut magnet again, seen in the drawing. So inside a magnet the field points from its S end towards its N end.
Hold an N pole and an S pole close together, facing each other, as in the gap of a U-shaped magnet, and the lines run straight across the gap from N to S, parallel and evenly spaced except near the edges. That is a uniform magnetic field, with the same strength and direction everywhere, like the field between two charged plates. The later pages of this topic put wires and moving charges "in a uniform magnetic field", and this is the field they mean.
Here is the picture in use, in the set-up of an experiment you will meet again in the Electromagnetic Induction topic.
A bar magnet is held upright above a flat, horizontal coil of wire, with its N pole at the bottom. The magnet is lowered, passes through the coil and carries on below it. Which way does the magnet's field pass through the coil, and how does its strength there change?
Above the coil: lines leave an N pole, so below the magnet's N pole they point down and spread out. The field through the coil points down. As the magnet comes closer, the coil sits where the lines are more crowded, so the field through it grows.
Inside the coil: while the magnet passes through, most of the lines through the coil are the ones inside the magnet, which run from S to N. The N pole is at the bottom, so these point down as well.
Below the coil: once the magnet has gone through, the coil is above its S pole. Lines enter an S pole, so above it they come down into it. The field through the coil still points down, and it weakens as the magnet falls away.
So the field through the coil points down the whole time. It grows while the N pole approaches and shrinks while the S pole leaves. The Electromagnetic Induction topic asks what a changing field like this does in the coil.
The Earth's magnetic field
A compass points north because the Earth has a magnetic field of its own, shaped much like the field of a huge bar magnet buried inside it. Follow the rule for poles carefully here. A compass's N pole points north, and an N pole is attracted to an S pole. So the magnetic pole near the geographic North Pole is a magnetic S pole, and a magnetic N pole lies near the geographic South Pole. The field lines leave the Earth in the southern hemisphere and come back in near the north. The mismatch in names is only history: the compass's N pole was named for where it points, long before anyone thought of the Earth as a magnet.
The Earth's magnetic poles are not quite at its geographic poles, so a compass points a little east or west of true north. The angle between the two directions is the magnetic declination (磁偏角), and the first written record of it is by the Chinese scholar Shen Kuo (沈括) in the 11th century. The field is not horizontal either: in the northern hemisphere its lines slope down into the ground as they head north. A compass lying flat shows only the horizontal part of the field, which points north.
Oersted's experiment: a current makes a magnetic field
For a long time electricity and magnetism looked like two separate subjects. In 1820 the Danish physicist Hans Christian Oersted (奥斯特) stretched a straight wire just above a compass needle and parallel to it, so that the wire ran north–south. When a current flowed in the wire, the needle swung away from north–south, towards a position at right angles to the wire. When he reversed the current, the needle swung the other way, and when he switched it off, the needle went back to north–south.
Nothing magnetic had been brought near the needle; only the current had changed. So a current sets up a magnetic field around itself, and reversing the current reverses the field. This was the first link ever found between electricity and magnetism, and the rest of this topic, and the next, grows from it. It also explains magnets. Ampère suggested that tiny circulating currents inside each particle of iron make it a tiny magnet, and that in a magnet these are lined up (分子电流假说, the molecular current hypothesis). Chinese textbooks sum it up: the field of a magnet and the field of a current both come from moving charge.
The field of a straight wire
To see the shape of the field, pass a long straight wire vertically through a horizontal card, sprinkle iron filings on the card, switch on a large current and tap the card. The filings settle into circles centred on the wire. Small compasses set on the card point along the circles, all the same way round, and when the current is reversed they all turn round to point the other way. So the field lines of a straight current are circles round the wire, lying in planes at right angles to it. Like a magnet's lines, they are closed loops.
The direction round the circles is given by the right-hand grip rule (安培定则, also called 右手螺旋定则). Grip the wire in your right hand with your thumb pointing along the current: your fingers curl round the wire the way the field lines go.
The filings show one more thing. They form clear circles close to the wire, and farther out the pattern fades, while a compass placed well away from the wire hardly turns from north–south. The field is strongest next to the wire and weakens with distance from it. Careful measurements show that the field is proportional to the current I and inversely proportional to the distance r from the wire, B ∝ I/r, so at twice the distance the field is half as strong. The papers have needed only the trend: nearer the wire, or with a larger current, the field is stronger.
A flat page needs a way to show directions into and out of it. A current or a field coming out of the page, towards you, is drawn as a dot, like the point of an arrow flying towards you. One going into the page is drawn as a cross, like the tail feathers of an arrow flying away. Seen end-on, a current coming out of the page has field lines going anticlockwise round it, and a current going into the page has them going clockwise. Seen from the side, with the wire in the plane of the page, the field lines go into the page on one side of the wire and come out of it on the other, as in Figure 2.
The circles also explain Oersted's set-up. Just below a wire, the field is horizontal and at right angles to the wire. With the wire running north–south, that field points east or west, straight across the needle, and turns it as far as it can. A wire running east–west would make a field along the needle, north or south, which pushes along the needle instead of across it and hardly turns it.
A long straight wire lies in the plane of the page, running from bottom to top, and carries a current up the page. Point P is 2 cm to the right of the wire, point Q is 6 cm to the right of it and point R is 2 cm to its left. Compare the field at the three points.
Direction: grip the wire with your right thumb pointing up the page. Your fingers come out of the page on the left of the wire, pass in front of it and go into the page on its right. So the field points into the page at P and Q, and out of the page at R.
Strength: P and R are the same distance from the wire, so the field is equally strong at both, though it points in opposite directions. Q is three times as far from the wire as P, so the field at Q is weaker: a third of the field at P, by B ∝ I/r.
If the current is reversed, all three fields reverse; their strengths do not change.
Loops and solenoids
Now bend the wire into a circular loop. Each short piece of the loop is nearly a straight wire, so the grip rule gives its field. The left of Figure 3 cuts the loop through its centre with the page: the current comes out of the page at the top and goes back into it at the bottom. Round the top the lines circle anticlockwise, and round the bottom clockwise. In the middle of the loop, between the two, both sets point the same way, to the right, so they add and the field through the middle is strong. Outside the loop the two sides' fields point opposite ways and partly cancel. The lines pass through the loop, come out of one face and curve round the outside back to the other face. A loop behaves like a thin, flat magnet, with its N face on the side where the lines come out.
For a loop the grip rule is used the other way round. Curl the fingers of your right hand round the loop the way the current flows; your thumb then points along the field through the middle of the loop, out of its N face.
A solenoid (螺线管) is a long coil: many loops wound side by side. Each turn adds its own loop field. Inside, the fields of all the turns point the same way along the axis, so the field inside is strong and, away from the ends, nearly uniform: its lines are straight, parallel and evenly spaced. Outside, the pattern is a bar magnet's, as on the right of Figure 3. The lines come out of one end, curve round and go back in at the other, and inside they run from the S end to the N end, exactly as inside a magnet. The grip is the same as for a loop: fingers round the turns the way the current flows, thumb along the field inside, pointing to the N end. Reverse the current and the poles swap.
A quick check needs no hand at all. Look at one end of a solenoid, or one face of a loop. If the current flows anticlockwise as you look at it, that end is an N pole; if it flows clockwise, an S pole. With the fingers curling anticlockwise as you look, the thumb points towards you, so the field comes out at you.
A solenoid lies on a table along an east–west line. Looking at its east end, you see the current flow clockwise round the turns. A compass is placed on the table just beyond the east end, on the solenoid's axis, where the solenoid's field is much stronger than the Earth's. Which end of the solenoid is its N pole, and which way does the compass point?
The poles: seen from the east, the current is clockwise, so by the end-on check the east end is an S pole and the west end is the N pole. The grip rule agrees. With the fingers curling clockwise as you look, the thumb points away from you, to the west, so the field inside points west and comes out of the west end.
The compass: just beyond the east end, the lines are heading into the S pole, so they point west, towards the solenoid. The compass's N pole points west, towards the solenoid. That fits the poles, since the compass's N pole is attracted to the solenoid's S end.
Reverse the current and both answers reverse: the east end becomes the N pole, and the compass turns to point east, away from the solenoid.
Your turn! · Practice questions
Things to remember
| Concept | What to know |
|---|---|
| Magnetic poles | Every magnet has an N pole and an S pole. Like poles repel, unlike poles attract. Poles come in pairs: cut a magnet and each piece has both. |
| Direction of the field | The way a compass's N pole points. The strength B is called the magnetic induction intensity or the magnetic flux density (磁感应强度); the next page measures it. |
| Field lines | The tangent gives the direction; crowded lines mean a strong field; lines never cross. Outside a magnet N → S, inside S → N, so every line is a closed loop. |
| Uniform field | Straight, parallel, evenly spaced lines, as between facing N and S poles close together. |
| The Earth's field | A compass's N pole points north, so a magnetic S pole is near the geographic North Pole. The two pairs of poles do not coincide: the declination. |
| Oersted's experiment | A current makes a magnetic field, and reversing the current reverses it. The wire runs north–south just above the needle, so its field crosses the needle. |
| Straight wire | Circles centred on the wire. Thumb along I, fingers give B. Weaker farther away, stronger with more current: B ∝ I/r. |
| Dots and crosses | A dot means out of the page, a cross into it. A current up the page has crosses to its right and dots to its left. |
| Loop and solenoid | Fingers along I in the turns; the thumb gives B inside and points to the N end. Inside a solenoid the field is strong and nearly uniform; outside it looks like a bar magnet's. |
| End-on check | A current flowing anticlockwise as you look means an N pole facing you; clockwise means an S pole. |
| Chinese names | 磁感线 field lines; 安培定则 or 右手螺旋定则 the grip rule, not to be confused with 右手定则 (induced current) or 左手定则 (Ampère force). |