7 min readConcept sheet1-mark MCQ and assertion-reason, and 2-mark questions on poles, the magnetic moment and cutting a magnet

The bar magnet: poles and magnetic moment

A bar magnet is a magnetic dipole: its N and S poles never exist alone. Its magnetic moment m points from S to N inside the magnet.

Magnetic dipole moment mA vector from the S pole to the N pole; SI unit A m² (same as J T⁻¹)

PolesLike poles repel, unlike poles attract; a freely hung magnet sets roughly north-south

No monopolesAn isolated N or S pole (a magnetic monopole) has never been found

Cutting a magnetEach piece is a complete magnet; cut across its length into n equal pieces, each has moment m/n

What we know about magnets

Every magnet has two poles, called north (N) and south (S). The pull is strongest near the poles.
Like poles repel and unlike poles attract.
A bar magnet hung freely by a thread settles roughly along the geographic north-south line. The end that points north is its N pole.
No isolated pole (magnetic monopole) has ever been found. Break a magnet and each piece gets its own N and S poles.
Magnets attract iron, cobalt, nickel and their alloys. They also push on moving charges and currents.

Activity: field pattern with iron filings and a compass

You need a bar magnet, a sheet of white paper, iron filings and a small plotting compass.

1
Place the magnet on the table and lay the sheet of paper over it.
2
Sprinkle iron filings thinly over the paper and tap the paper gently.
3
Observe: the filings crowd near the two ends and form curves running from one end to the other, like the field of an electric dipole.
4
Remove the filings. Place the compass near the N end and mark dots at both ends of its needle. Move the compass so its tail sits on the front dot, and mark again.
5
Join the dots into a smooth curve and add an arrow. Repeat from other starting points to get several field lines.
6
Result: the field lines leave the N end and enter the S end, and they are closest together near the poles.

Magnetic dipole moment

A bar magnet is a magnetic dipole: two equal and opposite poles a small distance apart. Its strength and direction are given by its magnetic dipole moment m. It is a vector pointing from the S pole to the N pole inside the magnet. Its SI unit is A m², also written J T⁻¹. In a uniform field the magnet feels a torque that turns m along the field. A current loop and a solenoid also have a magnetic moment, and they behave just like bar magnets.

What happens when a bar magnet is cut

How it is cut	What each piece is	Moment of each piece
Into 2 equal parts across its length (perpendicular to the axis)	A shorter complete magnet, with its own N and S poles	m/2
Into 2 equal parts along its length (parallel to the axis)	A thinner complete magnet, with its own N and S poles	m/2
Into n equal parts, either way	n complete magnets, each a weaker dipole	m/n

Worked example: cutting and joining magnets

Problem

A bar magnet of magnetic moment 2.0 A m² is cut into 4 equal pieces across its length. (a) Find the magnetic moment of each piece. (b) Two pieces are placed end to end in a line, N of one touching S of the other. Find the moment of the pair. (c) The same two pieces are placed side by side with their moments opposite. Find the moment now.

Working

(a) Each piece is a complete magnet with a quarter of the material, so m′ = m/4 = 2.0/4 A m² = 0.50 A m².
(b) Joined N to S in a line, both moments point the same way, so they add: 0.50 + 0.50 = 1.0 A m².
(c) Side by side and opposite, the moments cancel: 0.50 − 0.50 = 0.

Answer

(a) 0.50 A m² each; (b) 1.0 A m²; (c) zero

In real life

Fridge door seals, the clasp on a school bag and the speaker in your phone all use permanent magnets. A magnetic compass still guides trekkers in the Himalayas when there is no phone signal.

Exam angle

1 marks: “A bar magnet is cut into two equal halves across its length. What happens to the magnetic moment of each half?” It becomes m/2: each half is a complete magnet, with its own N and S poles and half the material.

2 marks: “What is the magnetic dipole moment of a bar magnet? Give its SI unit and direction.” It is a vector that measures the strength of the magnet and decides the torque on it in a field (τ = m × B). SI unit A m² (J T⁻¹). It points from the S pole to the N pole inside the magnet.

2 marks: “Explain why an isolated magnetic pole cannot be obtained by cutting a magnet.” New N and S poles form at the cut faces, so every piece is a complete dipole. Magnetism comes from tiny current loops of electrons, each a dipole. No monopole has ever been found.

Remember it

Cut a magnet, get more magnets, never a lone pole. m runs from S to N inside the magnet.