24  Magnetism

24.1 Syllabus inquiry question

  • How do magnets and currents create magnetic fields?
Feynman Insight

From The Feynman Lectures on Physics, Vol II, Chapter 13:

Magnetic fields are the way nature records the influence of moving charge. When charges move, the field changes its character and can push back.

24.2 Learning Objectives

  • Describe magnetic poles and field lines.
  • Use the right-hand grip rule to determine field direction.
  • Describe magnetic fields around a straight wire and solenoid.
  • Explain how electromagnets and magnetic domains work.
  • Calculate simple magnetic field strengths for wires and solenoids.

24.3 Content

24.3.1 Magnetic Poles and Fields

Magnets have two poles: north and south.

Magnetic Poles
  • Like poles repel; unlike poles attract
  • Magnetic poles always come in pairs (dipoles)
  • There are no magnetic monopoles—cutting a magnet creates two smaller dipoles

Magnetic field lines: - Form closed loops from north to south outside the magnet - Never cross each other - Line density indicates field strength - Direction is from N to S outside, S to N inside

24.3.2 Interactive: Bar Magnet Field

Visualising the magnetic field around a bar magnet:

24.3.3 The Earth’s Magnetic Field

The Earth behaves like a giant bar magnet:

  • Geographic North Pole is near the magnetic south pole
  • Compasses align with field lines
  • The field protects Earth from solar wind particles
Compass Behaviour

A compass needle points toward geographic north because its north-seeking pole is attracted to Earth’s magnetic south pole (located near geographic north).

24.3.4 Magnetic Fields Around Currents

A current-carrying wire creates circular magnetic field lines around it.

Right-hand grip rule: Thumb points in direction of conventional current; curled fingers show field direction.

For a long straight wire:

\[B = \frac{\mu_0 I}{2\pi r}\]

where: - \(B\) = magnetic field strength (T) - \(\mu_0 = 4\pi \times 10^{-7}\ \text{T·m/A}\) (permeability of free space) - \(I\) = current (A) - \(r\) = distance from wire (m)

24.3.5 Interactive: Magnetic Field Around a Wire

Key observation: Field lines form concentric circles around the wire. Closer to the wire, the field is stronger.

24.3.6 Solenoids and Electromagnets

A solenoid is a coil of wire that creates a strong, nearly uniform magnetic field inside:

\[B = \mu_0 n I\]

where: - \(n = N/L\) = number of turns per metre - \(N\) = total number of turns - \(L\) = length of solenoid (m)

24.3.7 Interactive: Solenoid Field

Solenoid Properties
  • Inside: nearly uniform field along the axis
  • Outside: weak, similar to a bar magnet
  • Polarity determined by right-hand grip rule (fingers follow current, thumb points to N pole)

24.3.8 Electromagnets

An electromagnet is a solenoid with a ferromagnetic core (iron):

  • The core becomes magnetised by the field
  • This greatly increases the field strength
  • The electromagnet can be switched on/off with current

Applications: motors, relays, MRI machines, maglev trains

24.3.9 Magnetic Materials and Domains

Magnetic domains are regions within ferromagnetic materials where atomic magnetic moments are aligned:

  • In unmagnetised material: domains point randomly, cancelling out
  • In magnetised material: domains align, creating net magnetic field
Affecting Magnetism

Magnetism can be reduced by: - Heating above the Curie temperature - Mechanical shock (hammer blows) - Alternating magnetic fields (degaussing)

24.3.10 Interactive: Magnetic Domains

24.4 Worked Examples

24.4.1 Example 1: Field around a straight wire

A long straight wire carries \(5.0\ \text{A}\). Find \(B\) at \(0.040\ \text{m}\) from the wire.

Solution:

  1. Use \(B = \frac{\mu_0 I}{2\pi r}\)

  2. Substitute: \(B = \frac{4\pi \times 10^{-7} \times 5.0}{2\pi \times 0.040}\)

  3. Simplify: \(B = \frac{2 \times 10^{-6}}{0.040} = 2.5 \times 10^{-5}\ \text{T}\)

  4. Field strength is 25 μT

24.4.2 Example 2: Solenoid field

A solenoid has \(400\) turns over \(0.20\ \text{m}\) and carries \(0.50\ \text{A}\). Find \(B\) inside.

Solution:

  1. Calculate turns per metre: \(n = N/L = 400/0.20 = 2000\ \text{m}^{-1}\)

  2. Use \(B = \mu_0 n I\)

  3. \(B = 4\pi \times 10^{-7} \times 2000 \times 0.50\)

  4. \(B = 4\pi \times 10^{-4} \approx 1.3 \times 10^{-3}\ \text{T}\) (or 1.3 mT)

24.4.3 Example 3: Solenoid polarity

A solenoid is viewed from one end and the current around the turns flows anticlockwise. Identify the pole at that end.

Solution:

  1. Apply right-hand grip rule: fingers follow current direction around the coil

  2. With anticlockwise current (when viewed from that end), thumb points out of the solenoid

  3. The thumb points to the north pole

  4. That end is the north pole

24.4.4 Example 4: Increasing solenoid field

State three ways to increase the magnetic field strength inside a solenoid.

Solution:

  1. Increase the current (\(B \propto I\))

  2. Increase turns per metre by adding more turns or reducing length (\(B \propto n\))

  3. Add a ferromagnetic core (iron core) to multiply the field

24.5 Common Misconceptions

Common Misconceptions
  • Misconception: Magnetic poles can be isolated. Correction: Cutting a magnet creates two smaller dipoles. No magnetic monopoles have been observed.

  • Misconception: Field lines show the path charges travel. Correction: Field lines show the direction of the magnetic field, not particle trajectories.

  • Misconception: Only permanent magnets create magnetic fields. Correction: Moving charges (currents) also create magnetic fields.

  • Misconception: Any metal is strongly magnetic. Correction: Only ferromagnetic materials (iron, cobalt, nickel) are strongly attracted to magnets.

  • Misconception: Electromagnets are weaker than permanent magnets. Correction: Electromagnets can be made much stronger than permanent magnets and can be switched on/off.

24.6 Practice Questions

24.6.1 Easy (2 marks)

State the direction of the magnetic field around a straight wire carrying current upward (out of the page).

  • Apply right-hand grip rule correctly (1)
  • Correct direction: anticlockwise when viewed from above (1)

Answer: Anticlockwise (when viewed from above / in the direction of current)

24.6.2 Medium (4 marks)

A wire carries \(8.0\ \text{A}\). Calculate the field strength \(0.060\ \text{m}\) from the wire.

  • Use correct formula: \(B = \mu_0 I / (2\pi r)\) (1)
  • Substitute values correctly (1)
  • \(B = (4\pi \times 10^{-7} \times 8.0) / (2\pi \times 0.060)\) (1)
  • \(B = 2.7 \times 10^{-5}\) T with correct unit (1)

Answer: \(2.7 \times 10^{-5}\) T (or 27 μT)

24.6.3 Hard (5 marks)

A solenoid has \(600\) turns over \(0.30\ \text{m}\) and current \(0.40\ \text{A}\). Find the field inside and state one way to increase it.

  • Calculate \(n = N/L = 600/0.30 = 2000\ \text{m}^{-1}\) (1)
  • Apply \(B = \mu_0 n I\) correctly (1)
  • \(B = 4\pi \times 10^{-7} \times 2000 \times 0.40\) (1)
  • \(B = 1.0 \times 10^{-3}\) T (or 1.0 mT) (1)
  • Valid method: increase current, add turns, add iron core (1)

Answer: \(B = 1.0\) mT; increase by adding iron core (or increase current or add more turns)

24.7 Multiple Choice Questions

Test your understanding with these interactive questions:

24.8 Summary

Key Takeaways
  • Magnetic poles always exist in pairs (dipoles)
  • Field lines form closed loops from N to S externally
  • Right-hand grip rule: thumb = current direction, fingers = field direction
  • Straight wire: \(B = \mu_0 I / (2\pi r)\)
  • Solenoid: \(B = \mu_0 n I\) where \(n = N/L\)
  • Magnetic domains explain permanent magnet behaviour
  • Electromagnets use ferromagnetic cores to amplify fields

24.9 Self-Assessment

Check your understanding:

After studying this section, you should be able to:

24.10 Module 4 Complete

Congratulations on completing Module 4: Electricity and Magnetism!

What you’ve learned
  • Electrostatics: charges, Coulomb’s law, electric fields
  • Electric circuits: current, voltage, resistance, Ohm’s law
  • Circuit analysis: Kirchhoff’s laws, internal resistance
  • Magnetism: magnetic fields from magnets and currents