Short on time? This page is the recap. For explanations, Figure 1 and the worked examples, use the full study guide.
Recap
- A magnetic field B is a vector field (unit: tesla, T). It is used to find forces on moving charges, currents and magnetic materials.
- Fields come from dipoles, never from a lone pole. Cutting a magnet gives two smaller dipoles.
- Like poles repel; unlike poles attract.
- B points the way the north end of a compass points. A compass (a dipole) tends to line up with the field.
- A dipole’s field gets weaker with distance.
- Dipoles come from moving charge: electrons orbiting and spinning in atoms.
- Permanent and induced magnetism are both alignment of dipoles in a system. Induced alignment disappears when the external field goes.
- Earth is modelled as a dipole. The magnetic pole near the geographic North Pole is a magnetic south pole.
Key relationships
| Idea | What to remember |
|---|---|
| Field-line rules | direction = tangent and arrow; closer lines = stronger B; lines never cross; every line is a closed loop |
| Bar magnet | outside: away from N, into S; inside: S to N |
| Adding fields | B_total is the vector sum; for perpendicular parts, B = √(B₁² + B₂²), angle from B₂ = tan⁻¹(B₁/B₂) |
| Vacuum permeability | μ₀ = 4π × 10⁻⁷ T·m/A ≈ 1.26 × 10⁻⁶ T·m/A (a constant) |
| Materials | ferromagnetic μ ≫ μ₀; paramagnetic μ slightly > μ₀; diamagnetic μ slightly < μ₀ |
| Material type | Examples | In a field | Afterwards |
|---|---|---|---|
| Ferromagnetic | Fe, Ni, Co | domains align, strong attraction | can stay magnetised |
| Paramagnetic | Al, Ti, Mg | weak alignment with B, weak attraction | alignment lost |
| Diamagnetic | all materials (main effect in Cu, water) | weak alignment against B, weak repulsion | nothing left |
Assumptions behind the answers
- “Direction of B” means the direction the north end of a small compass would point.
- Earth’s field is treated as a dipole field; real Earth’s field is only approximately a dipole.
- A material’s permeability μ is not a constant: it varies with temperature, orientation and field strength.
Mistakes to avoid
- Stopping field lines at the poles. Continue them inside, S to N.
- Saying a cut magnet gives a separate N piece and S piece.
- Calling Earth’s Arctic magnetic pole a north pole.
- Saying magnets attract all metals.
- Treating field lines as the paths of moving charges.
- Giving a magnetic force to a charge at rest.
Quick self-check
- Earth’s field somewhere is 5.0 × 10⁻⁵ T. What is that in μT? (50 μT)
- Which way does B point inside a bar magnet? (From the S end to the N end.)
- A sample is weakly pushed away from both poles of a strong magnet. What kind of material is it? (Diamagnetic.)
Next: practice questions.