Walk through it one step at a time — every idea comes alive in the live panel on the right. Iron filings curl into field lines, a coil lifts nails, a wire kicks, a charge curves, and a tiny DC motor spins, all themed and paced for calm reading.
1 — The magnetic field around a bar magnet
Scatter iron filings on paper over a bar magnet and tap it: the bits snap into curving lines. They are revealing the magnetic field — the region around the magnet where another magnet or moving charge feels a force.
- Field lines — drawn out of the north pole and into the south pole; close together where the field is strong (near the poles), spread out where it is weak.
- Flux density B — the strength of the field, measured in tesla (T). They never cross, and each one is a closed loop running through the magnet.
Exam point: like poles repel, unlike poles attract — and you can never get a single pole; break a magnet and each piece is a new north–south pair.
2 — Magnetic field of a current-carrying wire
Oersted's discovery: a current makes a compass needle swing. A straight current-carrying wire is wrapped in circular magnetic field lines centred on the wire.
Right-hand grip ruleGrip the wire with the right hand, thumb pointing along the current I —
your curled fingers point the way B circles the wire.
Double the current and the field doubles; move twice as far from the wire and the field halves: B ∝ I / r. The field has no poles — it is pure loops around the wire.
3 — The solenoid & electromagnet
Wind the wire into a coil — a solenoid — and all those circular fields add up. Inside the coil they line up into a strong, uniform field; outside it looks exactly like a bar magnet, with its own north and south ends.
- Electromagnet — a solenoid wound on a soft-iron core. The current makes it a magnet; switch off and it stops — that is how a scrapyard crane grabs and drops a car.
- Which end is north? Curl the right-hand fingers along the current in the turns; the thumb points to the north end.
Field inside a long solenoidB = μ₀ n I (n = turns per metre) — uniform along the axis
4 — Force on a conductor: F = B I L sinθ
Put a current-carrying wire across a magnetic field and the field pushes it — the motor effect. The wire's own field adds to the magnet's on one side and cancels on the other, so it is shoved toward the weak side.
Force on a conductorF = B I L sinθ
θ = angle between wire and field · maximum when wire ⟂ field (θ = 90°), zero when parallel
Fleming's left-hand rulethumb = Force (motion) · First finger = Field (N→S) · seCond finger = Current
worked — wire in a field
B = 0.4 T, I = 3 A, L = 0.2 m, θ = 90°?
F = 0.4 × 3 × 0.2 × 1 = 0.24 N
5 — Force on a moving charge: F = qvB
A current is just moving charge, so a single moving charge feels the same magnetic force. The force is always perpendicular to the velocity, so it changes the charge's direction but never its speed — it curves into a circle.
Force on a moving chargeF = q v B sinθ — perpendicular to both v and B
circular path: q v B = m v² / r → r = m v / (q B)
This is exactly how a mass spectrometer sorts ions and how charged particles spiral in a magnetic field. A stationary charge (v = 0) feels nothing — only moving charge is pushed.
worked — proton in a field
q = 1.6×10⁻¹⁹ C, v = 2×10⁶ m/s, B = 0.5 T, θ = 90°?
F = 1.6×10⁻¹⁹ × 2×10⁶ × 0.5 = 1.6×10⁻¹³ N
6 — Torque on a current loop: the DC motor
Place a current loop in a field: one side is pushed up, the other down — equal and opposite forces a distance apart make a torque that spins the loop. That is the heart of every electric motor.
Torque on a coilτ = B I A N sinθ (A = area, N = turns)
maximum when the coil plane is parallel to the field
- Split-ring commutator — reverses the current every half-turn so the torque always pushes the same way and the coil keeps spinning.
- Stronger spin — more turns, more current, a stronger magnet, or a bigger coil all increase the torque.
7 — The moving-coil galvanometer
A galvanometer is a motor that is not allowed to spin freely. A coil hangs between curved magnet poles and a soft-iron core, giving a radial field so the turning force is steady. A hairspring opposes the twist.
How it reads currentdeflection ∝ current: B I A N = k θ → θ ∝ I
the radial field keeps sinθ = 1, so the scale is evenly spaced (linear)
- Ammeter — galvanometer + a small shunt resistor in parallel to carry big currents.
- Voltmeter — galvanometer + a large resistor in series to read voltage.
8 — Field-strength factors
For a solenoid B = μ₀ n I, so the field grows when you give it more to work with. An iron core multiplies it many times over by adding the iron's own aligned field.
- More turns per metre (n) — each turn adds its own circular field; pack them closer and B rises.
- More current (I) — double the amps, double the field.
- A soft-iron core — the iron magnetises and adds enormously to the field, then lets go cleanly when the current stops.
Why soft iron? It magnetises and demagnetises easily — perfect for an electromagnet you switch on and off; steel would stay magnetic.
9 — Recap & applications
Every device here is the same physics reused: a magnetic field, and a force on the current or charge inside it.
- Field lines run N → S; flux density B in tesla; you cannot isolate a single pole.
- Right-hand grip rule for the circular field round a wire; B ∝ I / r.
- Solenoid = bar magnet you switch on/off; electromagnet on a soft-iron core.
- F = B I L sinθ, direction by Fleming's left hand — the motor effect.
- F = q v B on a moving charge → circular path, r = mv/(qB).
- τ = B I A N sinθ spins a coil → the DC motor + split-ring commutator.
- Galvanometer → ammeter (shunt) or voltmeter (series resistor).
| Device | The physics it uses |
|---|
| Electric motor | Torque on a current loop, τ = BIAN |
| Loudspeaker | Force F = BIL on a coil drives the cone in and out |
| MRI scanner | A huge, uniform B aligns the body's protons |
| Maglev / mass spectrometer | Force on moving charges & currents |