Magnetism is not a side topic. It is the mechanism behind the transformer in your power supply, the choke that keeps RF out of your microphone lead, the tuned circuit that picks one station out of the band, the meter that shows your output, and — once you reach the antenna lessons — the radiated wave itself. The syllabus names permanent magnets and electromagnets explicitly, and Section A asks about them every sitting. Start with the magnet, and the coil follows from it.
Permanent magnets, poles and lines of force
A bar magnet has two poles, north-seeking and south-seeking, and they cannot be separated — break the magnet in half and you get two smaller magnets, each with both poles. The rule for how they behave with each other is short: like poles repel, unlike poles attract.
The space around a magnet is mapped by lines of force, or lines of magnetic flux. The lines leave the north pole, curve round through the surrounding space, re-enter at the south pole and continue through the body of the magnet back to the north, so every line is a closed loop. Where they crowd together the field is strong; they never cross one another.
Flux is measured in webers, flux density in teslas. Both turn up in the paper as distractors against the henry, so know which is which.
The field around a current
Here is the connection between the two halves of the syllabus. Every current has a magnetic field circling it. Pass a current through an ordinary straight wire and a set of concentric circular lines of force appears around it, at right angles to the wire. Nothing needs to be coiled for this to happen; coiling only concentrates what is already there.
Two things follow. The field strength depends on the size of the current — double the current, double the field. And its direction depends on the direction of the current, which the right-hand grip rule gives you: grip the wire with your right hand, thumb pointing the way conventional current flows, and your curled fingers show the way the lines of force circle. Reverse the current and the circles reverse.
The solenoid and the electromagnet
Wind that wire into a cylindrical coil — a solenoid — and the fields of the individual turns add along the axis. The coil now behaves exactly like a bar magnet, with a north pole at one end and a south pole at the other, except that it can be switched off.
Slide a soft-iron core inside and the field becomes far stronger for the same current. That combination — coil plus iron core, energised by a current — is an electromagnet, and the syllabus asks about its uses:
- A relay: the electromagnet pulls an iron armature against a spring, closing or opening contacts. A small current controls a large one, and the two circuits stay electrically separate.
- A loudspeaker: a coil hanging in the gap of a permanent magnet carries the audio current, is attracted and repelled by the fixed magnet, and drags a paper cone with it to push the air. An earphone is the same idea with a magnetic diaphragm.
- A moving-coil meter: a pivoted coil in a permanent magnet's field turns a pointer against a hairspring by an amount proportional to the current. That is the movement behind every analogue ammeter, voltmeter and S-meter.
Permeability and magnetic materials
Permeability is a material's willingness to carry magnetic flux — the magnetic equivalent of conductivity. Free space has a permeability µ0 of 4π × 10⁻⁷ henries per metre, and every other material is quoted as a multiple of it, the relative permeability µr. Air is 1. Soft iron is in the thousands. That factor is exactly what a core multiplies the inductance by.
The exam separates two magnetic materials, and the difference is worth holding:
| Material | Magnetises | When the field is removed | Used for |
|---|---|---|---|
| Soft iron | Easily | Loses its magnetism at once | Electromagnets, relay cores, transformer cores — a temporary magnet |
| Hardened steel, alnico | With difficulty | Keeps it | Permanent magnets — loudspeakers, meters |
Electromagnetic induction
Everything so far has been current making a field. The reverse is the discovery radio is built on. Michael Faraday found that when the magnetic flux through a circuit changes, an EMF is induced in that circuit.
induced EMF = N × (change in flux ÷ time taken)
volts = turns × webers per second
Read the emphasis carefully, because it is a question: it is the change in flux that induces an EMF, not the flux itself. A coil lying motionless in the field of a permanent magnet generates nothing at all. Move the magnet, move the coil, or alter the current in a neighbouring coil, and the moment anything changes an EMF appears — and it stops the instant the movement stops.
Heinrich Lenz supplied the direction. The induced EMF always acts in the direction that opposes the change producing it. Push a magnet into a coil and the induced current sets up a field that pushes back at it; pull it out and the induced current tries to hold it in. Lenz's law is energy conservation wearing a disguise: if the induced EMF helped the change along instead of resisting it, you would have a machine that made energy out of nothing.
Self-inductance, the henry, and back EMF
A coil sits in its own magnetic field. So when the current through a coil changes, its own flux changes, and by Faraday's law an EMF is induced in the coil itself. By Lenz's law that EMF opposes the change. This self-induced voltage is the back EMF, and the property that produces it is self-inductance, symbol L, measured in henries.
V = L × (change in current ÷ time taken)
volts = henries × amperes per second
That gives the definition the examiner wants: a coil has an inductance of one henry when a current changing at one ampere per second induces one volt across it. The henry is a large unit — real coils are millihenries (mH) at audio and microhenries (µH) at RF.
What sets the inductance of a coil
L ∝ (N² × µ × A) ÷ l
| Change | Effect on L | Why |
|---|---|---|
| Double the turns, N | Four times | More turns make more flux and more turns for that flux to link — the effect enters twice |
| Insert a soft-iron or ferrite core | Rises sharply | The core's permeability concentrates far more flux through the same turns |
| Larger cross-sectional area, A | Rises | A wider loop encloses more flux |
| Stretch the winding out longer, l | Falls | The turns are further apart, so their fields help each other less |
Stretching or compressing an air-cored coil is a real adjustment: it is how a VHF coil is trimmed on the bench, and why such coils are varnished once set.
Energy stored — in the magnetic field
Building the field takes energy from the circuit, and collapsing it gives that energy back. The store is the magnetic field, which is the exact counterpart of the capacitor's electric field.
E = ½ × L × I²
joules = henries × amperes squared
Worked example 1 — energy in a choke
A 2 H smoothing choke carries 0.5 A. How much energy is held in its field?
E = ½ × 2 × 0.5² = ½ × 2 × 0.25 = 0.25 J
Interrupt that current abruptly and the field must dump 0.25 J somewhere in a fraction of a millisecond. It does so as a voltage spike across whatever broke the circuit.
The LR time constant
Because the coil fights the change, current in an inductive circuit does not start instantly either. It rises along the same exponential shape as the capacitor's voltage, governed by:
τ = L ÷ R
seconds = henries ÷ ohms
One time constant takes the current to 63.2 % of its final value, and it is treated
as fully established after five. Note that the resistance is on the bottom here
and on the top in τ = RC — a favourite way of setting a wrong option.
Worked example 2 — an LR circuit
A 10 mH coil is switched across a supply through a total resistance of 5 Ω.
τ = L ÷ R = 0.01 ÷ 5 = 0.002 s = 2 ms
The current reaches 63.2 % of its final value after 2 ms and is settled after about
5 × 2 = 10 ms.
Inductors in series and parallel
Provided the coils are far enough apart, or screened, that their fields do not interact, inductances combine exactly like resistors — which makes them the easy case, and makes capacitors the exception you have to remember.
Series: L = L₁ + L₂ + L₃ Parallel: 1/L = 1/L₁ + 1/L₂ + 1/L₃
Set the widget below to Inductors and compare it with the Capacitors setting on the same numbers. Two 10 mH coils in series give 20 mH; the same two in parallel give 5 mH.
Series and parallel two to four components
Enter two values.
Sanity rule: a series resistance is always larger than the largest resistor in the string; a parallel resistance is always smaller than the smallest resistor in the group. If your answer breaks that rule, the arithmetic is wrong. Inductors follow the same rule. Capacitors follow it upside down.
The proviso matters: coils close enough to share flux no longer obey the simple formulae, because how they are wound relative to each other starts to count.
Types of inductor
| Type | Core | Typical use |
|---|---|---|
| Air-cored | None | VHF and HF tuned circuits; no core losses, low values |
| Iron-cored (laminated) | Soft iron | Mains and audio work, smoothing chokes; useless at RF |
| Ferrite / dust-iron | Powdered magnetic ceramic | RF coils, chokes, baluns — high permeability without heavy core losses |
| Toroidal | Ring of ferrite or powdered iron | Compact, and the field stays inside the ring |
The toroid deserves its own sentence. Because the core is a closed ring, the flux path never leaves the material — the lines of force run round inside the doughnut and there is almost no external field. A toroid therefore induces nothing into its neighbours and picks nothing up from them, so parts can be packed close without screening cans. It is the standard core in a modern rig.
An RF choke is an inductor chosen to present a high opposition at radio frequency while passing DC almost freely — the mirror image of a capacitor. It is what stops RF running back down a power lead into your supply. That frequency-dependent opposition is inductive reactance, and it has its formula in Phase, Reactance, Impedance and Power Factor.
Mutual inductance and coupling
Put a second coil near the first. The changing field of coil one passes through coil two and induces an EMF there as well. That is mutual inductance, symbol M, also measured in henries: one coil acting on another, as against self-inductance, which is a coil acting on itself.
How much of the first coil's flux reaches the second is the coefficient of coupling, k, a number from 0 to 1. Two coils at right angles across the room have k near zero; two windings on one closed iron core have k near 1, called tightly coupled. A receiver's IF transformer is deliberately set part-way, because k controls the bandwidth of the coupled pair — an idea Series and Parallel Resonance takes up.
Mutual inductance with two windings and a good core is a transformer, and that is the whole of the next lesson.
Practice
Check yourself
1 / 10
Loading questions…
Kept in this browser only. Nothing is uploaded, and there is no account to make.
On the plan, not yet built
Should these lessons have video too?
Thirty-six lessons is the better part of eight hours of footage, and it is only worth recording if people would actually watch it rather than read. One tap tells me. Nothing else is asked of you.