Chapter 4 · Magnetic Effects of Electric Current

4.1 Magnets, Magnetic Fields and Field Lines

Every magnet fills the space around it with a magnetic field. A compass needle shows the field's direction at each point, and field lines — out of the north pole, into the south pole, never crossing — show its shape and its strength.

A fridge magnet holds a shopping list through a sheet of paper; a compass needle on a hiking trail swings round to point north; a hospital MRI scanner uses a magnet thousands of times stronger than any fridge magnet to take pictures of the inside of the body. In every case something reaches across empty space and pushes or pulls — without touching. Physicists describe that "reach" with one idea: the magnetic field.

In 1820 the Danish scientist Hans Christian Ørsted noticed that a compass needle swung whenever a current flowed in a wire near it. That chance observation joined electricity and magnetism into one subject, and it is the story of this chapter. Before we can see what a current does to a compass (Section 4.2), we need a clear picture of the field of an ordinary magnet: its poles, the direction of its field, and how to draw the field with field lines — first with a compass and pencil, then with iron filings.

Magnets and Magnetic Poles

Some rocks, such as magnetite (lodestone), are natural magnets. The magnets in a laboratory are artificial: bar magnets, horseshoe magnets, ring magnets and compass needles, made of steel or special alloys. Dip a bar magnet into iron filings and the filings cling in thick tufts at the two ends and hardly at all in the middle. The two regions where the attraction is strongest are the poles of the magnet.

Hang a bar magnet from a thread so that it can turn freely. It always comes to rest pointing roughly north–south. The end that points north is called the north-seeking pole or simply the north pole (N); the other end is the south pole (S). A compass needle is nothing more than a tiny, light bar magnet balanced on a pivot so that it can turn easily — its north pole is usually painted red or shaped like an arrowhead.

📐 Law 4.1 — The rules of magnetic poles
  1. A freely suspended magnet comes to rest along the north–south direction, its north pole pointing north.
  2. Like poles repel; unlike poles attract. N repels N and S repels S, but N attracts S. The force is stronger when the poles are closer.
  3. Poles always come in pairs. Cut a magnet in two and each piece is a complete magnet with its own N and S pole; no one has ever found a single, isolated pole.
  4. A magnet attracts magnetic materials such as iron, nickel, cobalt and steel, but not copper, aluminium, wood or plastic.

Rule 1 tells us something about the Earth: it behaves like a giant magnet. Since unlike poles attract, the north pole of a compass is pulled towards a magnetic south pole — so the Earth's magnetic south pole lies near the geographic North Pole. Rule 2 gives the only sure test of whether a bar is a magnet: an unmagnetised iron bar is attracted by either pole of a magnet, so attraction proves nothing. Only repulsion proves that both bodies are magnets.

✏️ Example 1 — Breaking a magnet
A bar magnet with its north pole on the left is broken into three equal pieces. How many magnets and how many poles are there now? Label the ends of every piece, from left to right.
Idea Poles always come in pairs (Law 4.1, rule 3), so every piece is a complete magnet with one N and one S pole.
Count Three pieces give $3$ magnets and $3\times2=6$ poles.
Labels Each piece keeps the orientation of the original: N S | N S | N S. Every new break face that was next to an N end is now an S pole, and the other side of the break is an N pole.
Check Neighbouring faces at each break are S and N — unlike poles — so the pieces still attract each other and click back together. ✓
✏️ Example 2 — Magnet or plain iron?
Three identical-looking bars P, Q and R are tested. The end of P attracts both ends of Q. One end of R repels one end of P. Which bars are certainly magnets? What can you say about Q?
Repulsion Repulsion happens only between like poles of two magnets, so P and R are both magnets.
Q One end of the magnet P attracts both ends of Q. If Q were a magnet, one of its ends would be a like pole and would be repelled. So Q is an unmagnetised piece of a magnetic material, such as soft iron.
Rule Attraction alone can never prove that a bar is a magnet — repulsion is the sure test.

The Magnetic Field and Magnetic Field Lines

Bring a compass slowly towards a bar magnet. Far away the needle points north as usual; closer in, it starts to turn, and near the magnet it lines up in a definite direction that changes from place to place. The magnet has changed the space around it: wherever you put the compass, there is a force on its poles. That region of influence is the magnetic field.

📘 Definition 4.1 — Magnetic field

The magnetic field of a magnet is the region around it in which its magnetic force can be detected — on a compass needle, another magnet or a piece of a magnetic material.

A magnetic field has both a strength and a direction. The direction of the field at a point is the direction in which the north pole of a compass needle placed at that point points. The field is written $B$.

A compass gives the direction at one point only. To see the whole field at a glance we draw curves that follow the compass from point to point.

📘 Definition 4.2 — Magnetic field lines

A magnetic field line is a curve drawn in a magnetic field so that the tangent to it at any point gives the direction of the field at that point — the direction in which a compass needle there would point. An arrow on the line shows that direction: outside a magnet, from the N pole towards the S pole.

🧭 Plotting a field line with a compass
  1. Fix a sheet of paper to the table, place a bar magnet in the middle and trace its outline. Mark its N and S ends. Keep other magnets and iron objects away.
  2. Place a small compass near the north pole. Mark a pencil dot at the position of the needle's north end.
  3. Move the compass so that its south end sits on that dot, and mark a new dot at its north end.
  4. Repeat, step by step, until you reach the south pole of the magnet (or the edge of the paper).
  5. Join the dots with a smooth curve and put an arrow on it in the direction the needle's north end pointed. That curve is one field line.
  6. Start again from a different point near the N pole to draw more lines. Interactive 1 shows exactly this method.
Interactive 1 — Compass Explorer around a Bar Magnet

Drag the compass anywhere around the magnet and watch its needle line up with the field; the readouts give the direction the north end points and how strong the field is compared with point X. Play runs the plotting method: the compass walks tip-to-tail along the field and leaves a pencil dot at each step, from the N pole round to the S pole. Flip the magnet to see every arrow reverse.

compass at—
needle's N end points—
field strength (× field at X)—
dots plotted—

Iron filings. A quicker way to see the whole pattern at once is to put a sheet of card over a magnet, sprinkle iron filings on it and tap the card gently. Each filing becomes a tiny magnet in the field and turns to line up with it, so the filings arrange themselves along the field lines. Where the field is strong they line up crisply and crowd together; where it is weak they stay jumbled. The pattern does not show the direction of the field — for the arrows you still need a compass.

📐 Result 4.2 — Properties of magnetic field lines
  1. Direction. Outside a magnet, field lines run from the north pole to the south pole; inside the magnet they run from the south pole to the north pole. So every field line is a closed, continuous curve — it has no beginning and no end.
  2. Tangent. The tangent to a field line at any point gives the direction of the field there.
  3. Strength. The field is stronger where the lines are closer together. Around a bar magnet they are most crowded near the poles, so the field is strongest there.
  4. No crossing. Two field lines never intersect. If they did, a compass at the crossing point would have to point in two directions at once, which is impossible: the field has only one direction at each point.
  5. Uniform field. Where the lines are parallel and equally spaced, the field is the same everywhere.
📘 Definition 4.3 — Uniform magnetic field

A magnetic field is uniform in a region if it has the same strength and the same direction at every point of that region. Its field lines are straight, parallel and equally spaced. The field in the gap between the flat poles of a horseshoe magnet, and the field inside a long current-carrying coil (Section 4.2), are very nearly uniform.

✏️ Example 3 — Where does the compass point?
A bar magnet lies on a table with its N pole to the east (right) and its S pole to the west. A compass is placed in turn at four points: A, on the axis a little beyond the N pole; B, on the axis a little beyond the S pole; C, just north of the middle of the magnet; D, just north of the N pole. In which direction does the needle's north end point at each? (Ignore the Earth's field.)
Idea The needle points along the field line through the point, and outside the magnet field lines run from N to S.
A and B At A the lines leave the N pole straight along the axis: the needle points east, away from the magnet. At B the lines enter the S pole along the axis: the needle points east again, now towards the magnet.
C Beside the middle of the magnet the lines run parallel to it, from the N end back towards the S end: the needle points west — opposite to the way the magnet's own N pole faces.
D Just above the N pole the lines spring outwards from the pole: the needle points roughly north, away from the pole.
Check Drag the compass in Interactive 1 to A, B, C and D. ✓
✏️ Example 4 — Why can't two field lines cross?
A student draws two field lines of a bar magnet crossing at a point P at right angles. Explain why the diagram must be wrong.
Meaning The tangent to each line at P gives the field direction at P. Two lines crossing at right angles would give two different directions, $90^\circ$ apart.
Physics A compass needle at P can settle in only one direction, so the field at P has only one direction.
Conclusion Through any point there passes only one field line; field lines never intersect.
✏️ Example 5 — Reading the strength from a diagram
In a field-line diagram, 12 field lines pass through a short gap $2.0\ \text{cm}$ wide at point A near a pole, and 4 lines pass through a gap of the same width at point B farther away. Compare the field strengths at A and B.
Idea The strength of the field is shown by how closely the lines are packed — the number of lines through a gap of fixed width.
Ratio $\dfrac{\text{strength at A}}{\text{strength at B}}=\dfrac{12}{4}=3$.
Answer The field at A is about $3$ times as strong as at B — as expected, since A is nearer the pole.
✏️ Example 6 — Two magnets face to face
Two identical bar magnets lie in a line with their north poles facing each other, $10\ \text{cm}$ apart. (a) Sketch the field lines in the gap. (b) Where is the field zero? (c) What changes if one magnet is turned round so that an N pole faces an S pole? (Ignore the Earth's field.)
(a) Lines leave both N poles, meet head-on in the gap and are pushed apart: they bend away sideways and curve round to the S ends of their own magnets. No line goes from one magnet to the other.
(b) By symmetry the two fields are equal and opposite exactly halfway: the field is zero at the neutral point, $5.0\ \text{cm}$ from each N pole. A compass there has no preferred direction.
(c) With N facing S, the lines run straight across the gap from the N pole to the S pole, crowded and nearly parallel: a strong, almost uniform field and no neutral point between them. The magnets now attract.
Check Choose "N facing N" and "N facing S" in Interactive 2. ✓
Interactive 2 — Iron Filings Lab

Choose an arrangement of magnets under the card and press Tap the card: the scattered filings turn to line up with the field — crisply where the field is strong, hardly at all where it is weak. Switch on the field lines to compare, and look for the neutral point. Play tours all four arrangements.

arrangement—
field strongest—
in the middle of the picture—
filings lined up—
⚠️ Common mistakes

1. "Field lines start at N and end at S." They do not end: outside the magnet they go from N to S, and inside the magnet they continue from S back to N. Field lines are closed curves.

2. "The compass points to the Earth's north magnetic pole." The needle's north pole is attracted, so it points towards a magnetic south pole — the one that lies near the geographic North Pole.

3. Attraction as a test. A magnet attracts plain iron too. Only repulsion proves that a bar is magnetised.

4. "There is no field between the lines." Field lines are a picture, not threads. The field exists everywhere around the magnet; we simply draw a few lines to show its shape, and their spacing to show its strength.

5. Arrows from iron filings. Filings show the pattern of the field but not its direction. Mark arrows only after checking with a compass.

🚀 Beyond the board syllabus (JEE Main · NEET · JEE Advanced) — optional: how strong is a magnetic field?

The magnetic field and its unit are in JEE Main, NEET and JEE Advanced 2026; the Earth's field and neutral points at the end are not listed in any of them; not in the CBSE Class 10 syllabus.

The SI unit of magnetic field is the tesla (T), named after the engineer Nikola Tesla. Some typical values:

SourceField, roughly
Earth's field at the surface$3\times10^{-5}$ to $6\times10^{-5}\ \text{T}$
A fridge magnet, at its surfaceabout $5\times10^{-3}\ \text{T}$
A strong neodymium magnet, at its surfaceabout $1\ \text{T}$
A hospital MRI scanner$1.5$ to $3\ \text{T}$

Near a laboratory magnet a compass feels the magnet's field and the Earth's field together. At certain points the magnet's field is exactly equal and opposite to the horizontal part of the Earth's field; the two cancel and the compass needle stays in any position it is given. These are also called neutral points, and locating them is a classic Class 12 experiment (Class 12 Physics, Magnetism and Matter).

Exercises

I
Magnets and their poles.
  • 1 What is a magnetic pole? Where are the poles of a bar magnet?
  • 2 A bar magnet hangs freely from a thread. In which direction does it come to rest, and what is the end pointing north called?
  • 3 What happens when (a) the N pole of one magnet is brought near the N pole of another; (b) an N pole is brought near an S pole; (c) an S pole is brought near a piece of soft iron?
  • 4 A bar magnet is broken into four pieces. How many magnets and how many poles are there?
  • 5 Why is repulsion, and not attraction, the sure test of whether a bar is a magnet?
  • 6 Which of these are attracted by a magnet: an iron nail, a copper wire, a steel pin, aluminium foil, a piece of nickel, a plastic ruler?
  • 7 Which kind of magnetic pole lies near the Earth's geographic North Pole? Explain.
  • 8 A compass on a laboratory bench points east instead of north. Suggest a reason.
Check: cut a bar magnet into equal pieces and read off the poles
4
magnets—
poles—
ends, left to right—
1 A pole is a region of a magnet where its attracting power is strongest. In a bar magnet the poles are near its two ends.
2 Along the north–south direction; the end pointing north is the north-seeking (north) pole, N.
3 (a) They repel. (b) They attract. (c) The iron is attracted — either pole attracts an unmagnetised magnetic material.
4 Every piece is a complete magnet: $4$ magnets and $4\times2=8$ poles.
5 A magnet attracts both another magnet (unlike poles) and plain iron, so attraction cannot tell them apart. Repulsion happens only between like poles of two magnets.
6 The iron nail, the steel pin and the nickel. Copper, aluminium and plastic are not magnetic materials.
7 A magnetic south pole: the compass's north pole points towards it, and unlike poles attract.
8 A magnet or a large iron object (a steel cupboard, a loudspeaker, a current-carrying cable) nearby produces a field stronger than the Earth's at that place, and the needle follows it.
II
The magnetic field and field lines.
  • 1 Define the magnetic field of a magnet.
  • 2 How is the direction of a magnetic field at a point found?
  • 3 What is a magnetic field line?
  • 4 Why are magnetic field lines called closed curves?
  • 5 Why do two magnetic field lines never intersect?
  • 6 Where is the field of a bar magnet strongest, and how does the field-line diagram show it?
  • 7 How is a uniform magnetic field shown on a diagram? Name one place where such a field is found.
  • 8 In a diagram, $18$ lines cross a $3.0\ \text{cm}$ gap at P and $6$ lines cross a $1.0\ \text{cm}$ gap at Q. Where is the field stronger?
  • 9 Can the pattern of iron filings tell you the direction of a field? Explain.
1 The region around a magnet in which its magnetic force can be detected (on a compass, another magnet or a magnetic material).
2 Place a small compass at the point: the field points the way the needle's north end points.
3 A curve drawn so that its tangent at every point gives the direction of the magnetic field there.
4 Outside the magnet they go from N to S and inside it from S back to N, so each line closes on itself with no start or end.
5 At a crossing the field would have two directions, so a compass would have to point two ways at once — impossible.
6 Near the poles; the lines are most crowded there.
7 By straight, parallel, equally spaced lines. Examples: between the flat poles of a horseshoe magnet; inside a long solenoid.
8 P: $\tfrac{18}{3.0}=6$ lines per cm; Q: $\tfrac{6}{1.0}=6$ lines per cm. The field is equally strong at P and Q — compare lines per unit width, not raw counts.
9 No. The filings line up along the field but either end of a filing could point either way; the direction must be found with a compass.
III
Plotting and field patterns.
  • 1 List the steps for plotting one field line of a bar magnet with a small compass.
  • 2 Why should the plotting compass be small?
  • 3 Why must iron objects and other magnets be kept away while plotting?
  • 4 Sketch the field lines of a bar magnet, with arrows both outside and inside the magnet.
  • 5 Sketch the field between an N pole and an S pole facing each other a short distance apart. Describe the field in the gap.
  • 6 Two identical bar magnets lie in a line with N facing N, $12\ \text{cm}$ apart. Where is the neutral point? (Ignore the Earth's field.)
  • 7 A compass is placed on the axis of a bar magnet, just beyond its S pole. Which way does the needle's north end point?
  • 8 Correct the statement: "Magnetic field lines begin at the north pole and end at the south pole."
1 Trace the magnet; put the compass near N; dot at the needle's north end; move the compass until its south end is on the dot; dot again; repeat to the S pole; join the dots smoothly and add an arrow in the needle's direction.
2 A small needle samples the field at almost a single point, and its own field disturbs the magnet's field less; the dots are close together, giving a smooth curve.
3 Their fields would add to the magnet's field and bend the plotted lines.
4 Closed loops leaving the N end, curving round on both sides and entering the S end; inside the magnet, straight lines from S to N; lines crowded near the poles, none crossing.
5 Straight, parallel, closely spaced lines from N across to S, bulging slightly at the edges: the field in the gap is strong and nearly uniform.
6 Halfway, $6.0\ \text{cm}$ from each N pole, where the two equal fields are opposite.
7 Towards the magnet (towards its S pole) — field lines enter the S pole.
8 "Outside a magnet, field lines go from the north pole to the south pole; inside it they continue from the south pole to the north pole, so they form closed curves with no beginning or end."
IV
Magnets in everyday life.
  • 1 The rubber seal of a fridge door contains a magnetic strip. Why does the door stick to the steel cabinet? Would it stick to a wooden cabinet?
  • 2 Why should a compass be kept away from loudspeakers and mobile phones?
  • 3 A magnetised screwdriver picks up steel screws but not brass ones. Explain.
  • 4 Ring magnets slid onto a pencil can float one above another without touching. Which faces must be next to each other? Explain.
  • 5 A ship's compass is mounted as far as possible from the steel hull and engines. Why?
  • 6 Challenge. You have two identical-looking steel bars, one magnetised and one not, and nothing else. How can you find which is the magnet?
1 Steel is a magnetic material, so the magnetic strip attracts it and the door is held shut. Wood is not magnetic, so it would not stick.
2 Both contain magnets whose fields, close up, are much stronger than the Earth's field; the needle would follow them and give a false direction (and a strong magnet can even weaken the needle's own magnetism).
3 Steel is a magnetic material and is attracted; brass (copper and zinc) is not.
4 Like poles — N facing N or S facing S. Like poles repel, and the repulsion holds the upper ring up against its weight.
5 Steel becomes magnetised in the Earth's field and the engines carry currents; both produce fields that would deflect the compass.
6 Touch one end of bar A to the middle of bar B. If they attract strongly, A is the magnet (its pole attracts the iron of B). If there is little or no attraction, B is the magnet: the middle of a magnet has almost no magnetism, and A, being plain steel, has no pole of its own.
🎯 Exam corner — board and entrance-exam practice BoardNEETJEE Main

E1. Board · 2 marks Why do two magnetic field lines never intersect? Where is the magnetic field of a bar magnet strongest?

Reason The tangent to a field line gives the field direction. At a crossing point there would be two tangents, so a compass needle there would point in two directions at once — impossible. [1 mark]
Answer The field is strongest near the poles, where the field lines are most crowded. [1 mark] Exam tip: always say "a compass would point in two directions" — that phrase is what the marking scheme looks for.

E2. Board · 3 marks Draw the pattern of magnetic field lines around a bar magnet. State two properties of magnetic field lines that your diagram shows.

Diagram A rectangle labelled N and S; several closed curves leave the N end, loop round above and below the magnet and enter the S end, with arrows from N to S outside and from S to N inside; lines crowded near the poles; no two lines crossing. [1½ marks]
Properties Any two of: field lines are closed curves (N to S outside, S to N inside); they never intersect; they are closer together where the field is stronger; the tangent gives the field direction. [1½ marks]
Exam tip Marks are lost for missing arrows and for lines that touch or cross. Draw at least three lines on each side of the magnet.

E3. Board · Assertion–Reason Assertion (A): Magnetic field lines are closed curves. Reason (R): Magnetic field lines start at the north pole and end at the south pole of a magnet. (A) Both A and R are true and R explains A. (B) Both are true but R does not explain A. (C) A is true but R is false. (D) A is false but R is true.

Idea A is true. R is false: the lines do not end at the S pole — they continue inside the magnet from S to N. A line that "ended" would not be a closed curve.
Answer (C). Exam tip: in assertion–reason items, check R on its own first; a reason that contradicts the assertion is usually false.

E4. Board · Case study Riya places a bar magnet on a sheet of paper and uses a small compass to plot its field. (i) Describe how she moves the compass from one plotted point to the next. [2 marks] (ii) In which direction does the needle point when the compass is beside the middle of the magnet? [1 mark] (iii) Her lines come out bent towards a steel cupboard nearby. Explain. [1 mark]

(i) She marks a dot at the north end of the needle, then moves the compass so that the south end of the needle lies on that dot, and marks the new position of the north end; repeating this traces the line from N towards S.
(ii) Parallel to the magnet, pointing from the N end towards the S end — opposite to the direction the magnet itself points.
(iii) The steel of the cupboard is magnetised by the magnet's (and the Earth's) field, and its own field adds to the magnet's, bending the plotted lines. Exam tip: in plotting questions, "south end on the previous dot" is the key step.

E5. NEET Which statement about magnetic field lines is incorrect? (A) They are closed curves. (B) Their tangent at a point gives the field direction there. (C) Inside a bar magnet they run from the north pole to the south pole. (D) They are crowded where the field is strong.

Check (A), (B) and (D) are correct properties. Inside a magnet the lines run from S to N, so (C) is wrong.
Answer (C). Exam tip: "N to S" is true only outside the magnet.

E6. JEE Main A bar magnet is cut along its length into two halves, and each half is then cut across into two pieces. How many complete magnets and how many poles are there? (A) $2$ magnets, $4$ poles (B) $4$ magnets, $4$ poles (C) $4$ magnets, $8$ poles (D) $8$ magnets, $8$ poles

Idea Every piece of a magnet, however it is cut, is a complete magnet with an N and an S pole.
Count One cut along the length gives $2$ thin magnets; cutting each across gives $4$ magnets in all, with $4\times2=8$ poles.
Answer (C). Exam tip: number of poles $=2\times$ number of pieces — there are no single poles.
🔬 Research–Teaching NexusResearch-tutored · optional, about 45 minutes

Research question. How much do the steel and wiring of a building distort the magnetic field that a compass — or your phone's map app — relies on?

Why it matters. Smartphones, drones and car navigation systems all contain a tiny magnetic-field sensor (a magnetometer) that works as an electronic compass. Steel beams, reinforced concrete and electrical cables make "magnetic noise" that can turn a map the wrong way. Pilots, ships' navigators and even migrating birds and sea turtles depend on reading the Earth's field correctly, and engineers who design hospitals with MRI scanners must keep strong fields away from corridors and lifts.

What to do.

  1. Install a free magnetometer app (many "sensor" or "physics toolbox" apps show the field in microtesla). Note the reading in an open field or playground, far from buildings and cars — that is roughly the Earth's field.
  2. Walk slowly along a corridor at home or school, holding the phone at the same height, and record the reading every metre. Mark the positions of steel doors, columns, radiators and wall sockets.
  3. Lay a small compass on the floor at the same points and note how far it turns from true north.
  4. Plot the field reading and the compass error against position. Where are the biggest disturbances, and what is nearby?

Tools: smartphone with a magnetometer app, small compass, metre tape, spreadsheet.

Hand in: A map of the corridor with readings marked, a graph of field and compass error against position, and a paragraph explaining two of the biggest disturbances.

Going further. Hold a bar magnet at increasing distances from the phone and record the reading. Roughly how quickly does the field fall off with distance? (You will meet the answer in Class 12 Physics, Magnetism and Matter.)

Instructor note: the Earth's field over India is roughly $40$–$50\ \mu\text{T}$; indoors, readings of $20$–$100\ \mu\text{T}$ near steel are common. Students should keep the phone flat and at a fixed height, since the sensor reads all three components. For a bar magnet on its axis the field falls roughly as the inverse cube of distance at large distances — doubling the distance gives about one-eighth — which students can discover from a log–log plot or by simple ratios.

🧪 Self-check quiz

0/5 correct

Q1. The direction of the magnetic field at a point is the direction in which

Q2. Inside a bar magnet, the magnetic field lines run

Q3. Two magnetic field lines cannot cross because

Q4. A bar magnet is broken into three pieces. The total number of poles is

Q5. A uniform magnetic field is shown by field lines that are

← Chapter 4 — Magnetic Effects of Electric Current4.2 Magnetic Field due to a Current: Wire, Loop and Solenoid →