Magnetism: Magnets, Magnetic Fields, the Earth's Field and Electromagnetism

What is a magnet?

A magnet attracts iron, steel, nickel and cobalt and, when freely suspended, comes to rest pointing north–south.

Magnetic materials

• Ferromagnetic: strongly attracted and can be made into magnets. Examples: iron, steel, nickel, cobalt.
• Paramagnetic: weakly attracted by a strong magnet. Examples: aluminium, platinum, manganese, oxygen.
• Diamagnetic: weakly repelled by a strong magnet. Examples: copper, bismuth, gold, water, glass.
• Everyday "non-magnetic" materials: wood, plastic, rubber, brass, paper.

Properties of magnets and the law of magnetism

• Attractive property: magnets attract magnetic materials, most strongly near the ends (poles).
• Directive property: a freely suspended magnet rests in the N–S direction.
• Poles always come in pairs: breaking a magnet gives two complete smaller magnets, never a single pole.

Law of magnetism: like poles repel; unlike poles attract.

Domain theory

• A ferromagnetic material contains tiny regions called domains, each acting like a tiny magnet.
• Unmagnetised: the domains point in random directions and cancel out.
• Magnetised: the domains line up in one direction and their effects add up.
• Saturation: when all the domains are aligned, the magnet cannot get any stronger.

Domain theory explains why heating or hammering a magnet destroys its magnetism (the domains are shaken back into random order), and why breaking a magnet gives two magnets.

Magnetisation and demagnetisation

To magnetise: single-touch or divided-touch stroking, induction, or the electrical method (place the steel bar in a solenoid carrying a steady direct current for a short time). The electrical method is the best.

To demagnetise: strong heating, hammering (in the east–west direction), rough handling, or (best) placing the magnet in a solenoid carrying alternating current, with the magnet pointing east–west, and slowly withdrawing it.

Soft iron vs steel

• Soft iron magnetises and demagnetises easily, so it makes temporary magnets. Uses: electromagnet cores, transformer cores, keepers, magnetic shields.
• Steel is harder to magnetise but keeps its magnetism, so it makes permanent magnets. Uses: compass needles, loudspeakers, motors.

Storing magnets: keep them in pairs with unlike poles side by side and soft-iron keepers across the ends.
Magnetic shielding: field lines crowd into a soft-iron ring or box, leaving the space inside almost field-free (protects watches and meters).

Magnetic fields and field lines

A magnetic field is the region around a magnet where a magnetic force can be felt. A line of force is the path a free north pole would follow.

Properties of field lines:

• Outside a magnet they run from N to S.
• They never cross.
• They are closer together where the field is stronger (near the poles).
• They form closed loops through the magnet.

Plotting: iron filings show the pattern quickly; a plotting compass shows the direction (mark where the needle points, move it on, and join the dots).

A neutral point is where the magnet's field and the Earth's field are equal and opposite, so the resultant field is zero. A compass there points in no particular direction.

• Magnet with its N-pole pointing north: neutral points lie on the equatorial line (east and west of the magnet).
• Magnet with its N-pole pointing south: neutral points lie on the axis.

The Earth's magnetic field

The Earth behaves like a giant magnet. Its magnetic south pole lies near the geographic North Pole, which is why it attracts the north pole of a compass.

• Magnetic meridian: the vertical plane containing a freely suspended compass needle.
• Geographic meridian: the vertical plane through the place and the geographic poles.
• Angle of declination (variation): the angle between the magnetic and geographic meridians.
• Angle of dip (inclination): the angle the Earth's field makes with the horizontal. It is 0° at the magnetic equator and 90° at the magnetic poles. It is measured with a dip circle.

Components of the Earth's field (B = total field, θ = angle of dip):

• Horizontal: B_H = B cos θ
• Vertical: B_V = B sin θ
• tan θ = B_V ÷ B_H and B² = B_H² + B_V²

The magnetic effect of a current

A current-carrying conductor is surrounded by a magnetic field (Oersted's discovery).

• Straight wire: the field lines are concentric circles round the wire. Right-hand grip rule: grip the wire with your right hand, thumb along the current; your curled fingers show the field direction.
• Solenoid (coil): the field is like a bar magnet's. Looking at one end, an anticlockwise current makes that end a north pole; clockwise makes it a south pole.

The field of a solenoid is made stronger by: more turns, a larger current, and a soft-iron core.

Electromagnets

An electromagnet is a soft-iron core inside a coil. It is magnetic only while current flows, so it can be switched on and off.

The electric bell: pressing the switch lets current flow → the core becomes a magnet and attracts the soft-iron armature → the hammer strikes the gong → the armature leaves the contact screw, breaking the circuit → the core loses its magnetism → the spring pulls the armature back, remaking the contact → the cycle repeats rapidly.

Other uses: relays and circuit breakers, magnetic cranes in scrapyards, telephone earpieces, loudspeakers, MRI scanners, maglev trains.

Force on a current-carrying conductor

A conductor carrying a current in a magnetic field experiences a force:

F = BIL sin θ

• B = magnetic flux density (tesla, T); I = current (A); L = length of conductor in the field (m); θ = angle between the conductor and the field.
• Maximum force when θ = 90°: F = BIL.
• Zero force when the conductor is parallel to the field (θ = 0°).

Fleming's left-hand rule: hold the thumb, first finger and second finger of your left hand at right angles. First finger → Field; seCond finger → Current; thuMb → Motion (force).

The tesla: 1 T is the flux density in which a conductor 1 m long, carrying 1 A at right angles to the field, experiences a force of 1 N.

Parallel currents: two parallel wires carrying currents in the same direction attract; currents in opposite directions repel.

Force on a moving charge

A charge q moving with velocity v in a field B experiences:

F = qvB sin θ

The force is always at right angles to the velocity, so it does no work: the speed and kinetic energy stay constant, but the direction changes. A charge moving at right angles to the field travels in a circle of radius r = mv ÷ (qB).

The d.c. motor and the moving-coil galvanometer

d.c. motor: the currents in the two sides of the coil flow in opposite directions, so they feel equal and opposite forces (a couple) and the coil turns. The split-ring commutator reverses the current every half-turn, so the coil keeps turning in the same direction. Energy change: electrical → mechanical.

A motor turns faster with: a larger current, more turns on the coil, a stronger magnet, or a larger coil area.

Moving-coil galvanometer: works on the same principle. Curved pole pieces and a soft-iron cylinder give a radial field, so the deflection is proportional to the current and the scale is uniform (linear). It becomes an ammeter with a low-resistance shunt in parallel, or a voltmeter with a high-resistance multiplier in series.

Magnetic flux

• Magnetic flux Φ = BA cos θ, where θ is the angle between the field and the normal to the area. Unit: weber (Wb).
• Flux density B = Φ ÷ A. Unit: tesla, where 1 T = 1 Wb m^-2.
• Flux linkage of a coil of N turns = NΦ.

Permanent magnet or electromagnet?

• Scrapyard crane: electromagnet (very strong and can be switched off to drop the load).
• Compass needle: steel permanent magnet (keeps its magnetism without power).
• Transformer or bell core: soft iron (magnetises and demagnetises easily).
• Protecting a watch: a soft-iron case (magnetic shield).

Summary formulas

• F = BIL sin θ
• F = qvB sin θ and r = mv ÷ qB
• B_H = B cos θ, B_V = B sin θ, tan θ = B_V ÷ B_H
• Φ = BA cos θ (Wb); flux linkage = NΦ
• 1 T = 1 N A^-1 m^-1 = 1 Wb m^-2

Practice

1. Which of these is NOT a magnetic material: iron, nickel, cobalt, copper?
2. What is the angle of dip at the magnetic equator?
3. A wire 0.5 m long carries 4 A at right angles to a 0.3 T field. Find the force on it.
4. A 25 cm wire carrying 8 A lies at 60° to a 0.5 T field. Calculate the force on it.
5. At a place, B_H = 3.0 × 10^-5 T and the angle of dip is 60°. Find B_V and the total field B.
6. A proton moves at 3 × 10⁵ m/s at right angles to a 0.2 T field. Find the force on it (e = 1.6 × 10^-19 C).
7. What is the best way to demagnetise a magnet?

Answers: 1. Copper · 2. 0° · 3. F = 0.3 × 4 × 0.5 = 0.6 N · 4. F = 0.5 × 8 × 0.25 × sin 60° ≈ 0.87 N · 5. B_V = B_H tan 60° ≈ 5.2 × 10^-5 T; B = B_H ÷ cos 60° = 6.0 × 10^-5 T · 6. F = qvB = 9.6 × 10^-15 N · 7. Place it in a solenoid carrying a.c., pointing east–west, and withdraw it slowly.

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