• Magnetic flux density (B) measures how strong a magnetic field is, in tesla.
• Magnetic flux (Φ) measures how much field passes through an area: Φ = BA.
• Flux linkage (NΦ) is flux × number of turns — used for coils.
• A moving charged particle in a field feels a force F = BQv sin θ — always perpendicular to its velocity, so it moves in a circle.
• A current-carrying wire in a field feels a force F = BIL sin θ.
• Fleming's Left Hand Rule gives the direction of that force from B and I (or v).
• Electromagnetic induction: a changing flux linkage induces an e.m.f in a circuit — this is how generators and transformers work.
• Faraday's Law gives the size of the induced e.m.f: ε = Δ(NΦ)/Δt.
• Lenz's Law gives the direction: the induced e.m.f always opposes the change that caused it (hence the minus sign).

Think of a magnetic field as invisible field lines spreading out from a magnet. Where the lines are packed tightly together, the field is strong. Where they're spread apart, it's weak. Magnetic flux density, B, is simply the official number that tells you exactly how strong the field is at a point — it's basically "how densely packed are the field lines here?" It's measured in tesla (T), and for reference, Earth's own magnetic field is a puny 0.032 mT, while an ordinary fridge magnet is about 5 mT — magnetic fields you actually notice tend to be much stronger than the one holding the compass needle north.

Flux density tells you how strong the field is at a point. Magnetic flux takes it a step further — it tells you how much of that field is actually passing through a specific area, like a hoop or a coil face. Picture holding a net in a stream of water: if you hold the net face-on to the flow, loads of water passes through it. Tilt the net so it's edge-on to the flow, and almost no water gets through, even though the stream itself hasn't changed at all. Magnetic flux works exactly the same way — same field, but how much of it "counts" depends entirely on the angle of the surface you're measuring through.

Real coils aren't just a single loop of wire — they're wound with many turns, often hundreds. If flux Φ passes through one loop, and there are N identical loops stacked on top of each other, then the total effect across the whole coil is N times bigger. That total is called flux linkage. It's the quantity that actually determines how much e.m.f gets induced in a coil (you'll see why in Topic 6) — more turns means more induced voltage for the same changing field.

Here's a fact that surprises a lot of students: a stationary charged particle sitting in a magnetic field feels nothing at all. Magnetic fields only push on charges that are moving. And crucially, the push doesn't happen in the direction of motion, or in the direction of the field — it happens sideways, perpendicular to both. This is what makes charged particles curve into circles instead of speeding up or slowing down.

Formulas tell you the size of the force, but not which way it points. For that, you need Fleming's Left Hand Rule. Hold your left hand so your thumb, first finger, and second finger are all at right angles to each other, like the three edges of a box meeting at a corner:

• First finger = direction of the magnetic Field (B)
• SeCond finger = direction of conventional Current (I) — always the direction of positive charge flow
• ThuMb = direction of Motion / force (F)

Remember it as FBI: First finger = B, seCond finger = I, thuMb = Motion.

A current-carrying wire is really just a huge crowd of moving charged particles (electrons) all travelling together. Since each individual charge feels a sideways magnetic force (Topic 2), and there are billions of them moving together inside the wire, the entire wire feels a sideways push too. This is the exact same physics as Topic 2 — just scaled up from one particle to a whole wire full of them, and rewritten in terms of current I instead of individual charge Q and velocity v.

Fleming's Left Hand Rule applies here exactly as before — first finger = B, second finger = I (conventional current), thumb = force. It's the same three-fingers-at-right-angles trick, just now the "current" finger points along the actual wire instead of along a single particle's velocity.

Everything so far has been about magnetic fields pushing on things. Now we flip it around: can motion through a magnetic field create electricity? Yes — this is electromagnetic induction, and it's arguably the single most useful idea in this whole chapter, because it's how every power station generator on Earth actually makes electricity.

Notice the key word: changes. A stationary magnet sitting inside a stationary coil induces absolutely nothing, no matter how strong it is. It's only when the flux linkage through the coil is changing — because the magnet is moving, the coil is rotating, or the field itself is varying — that an e.m.f gets induced. This can happen two ways: either a conductor physically cuts through field lines, or the flux through a coil changes because the field's strength, angle, or the coil's area changes.

Picture a bar magnet connected to nothing, and a coil connected to a sensitive voltmeter, with the magnet free to slide in and out of the coil. Here's what's actually observed:

• Magnet held still (inside or outside the coil) → voltmeter reads zero. No change in flux = no induced e.m.f.
• Magnet moving into the coil → voltmeter shows a reading. Field lines are "cutting through" the coil, generating a changing flux.
• Magnet moving out of the coil → voltmeter shows a reading of the opposite sign. Reversing the direction of change reverses the induced current.
• Moving the magnet faster → bigger reading, because the flux is changing more quickly.

Three things increase the size of the induced e.m.f: moving the magnet faster through the coil, adding more turns to the coil, and using a stronger magnet.

This is the actual mechanism behind an AC generator. Spin a coil inside a uniform magnetic field, and the flux through the coil constantly changes as the angle changes — maximum flux when the coil face is perpendicular to the field, zero flux when it's parallel. Because flux linkage keeps changing throughout the rotation, an e.m.f is continuously induced — and because the rotation keeps reversing which way flux is increasing or decreasing, that e.m.f keeps flipping sign. The result is an alternating voltage.

Spinning the coil faster (increasing its frequency of rotation) increases both the frequency and the amplitude of the alternating voltage produced.

What if instead of moving a magnet by hand, you used a second coil of wire to create the changing field? That's exactly what a transformer does. It has a primary coil, a secondary coil, and both are wrapped around a shared soft iron core. The iron core is essential — it's easily magnetised and demagnetised, so it efficiently channels the changing magnetic field from the primary coil straight through to the secondary coil, linking them magnetically even though they aren't electrically connected at all.

Here's the chain of events: alternating current flows in the primary coil → this creates an alternating magnetic field in the iron core → that changing field passes through to the secondary coil → the changing flux linkage in the secondary coil induces an e.m.f in it (by Faraday's Law, Topic 6) → this produces an alternating output voltage at the same frequency as the input.

We've talked about induction qualitatively — now for the maths. Faraday's Law connects the rate of change of flux linkage to the size of the induced e.m.f. It makes intuitive sense: the faster the flux linkage changes, the bigger the "kick" of voltage you get — exactly like how yanking a magnet quickly through a coil gives a much bigger voltmeter reading than sliding it slowly.

Faraday's Law tells you the size. Lenz's Law tells you the direction — and it's a beautifully strange rule once you understand it: nature is "lazy" about induction. Whatever gets induced will always try to fight against the very change that created it.

Push a north pole into a coil, and the coil will induce its own current in exactly the direction needed to make its near face into a north pole too — because two north poles repel, actively resisting the magnet's entry. Pull the magnet back out, and the coil flips its induced polarity to attract the magnet instead, resisting its exit. The coil is always fighting to keep the flux exactly as it was.

• I can define magnetic flux density and state its units (T).
• I can calculate magnetic flux using Φ = BA cos(θ), correctly identifying the angle from the normal.
• I can calculate flux linkage NΦ = BAN for a multi-turn coil.
• I can use F = BQv sin θ and explain why the force is maximum at 90° and zero at 0°.
• I can explain why the magnetic force on a moving charge causes circular motion (it's a centripetal force).
• I can apply Fleming's Left Hand Rule to a charged particle, remembering current = direction of positive charge flow.
• I can use F = BIL sin θ for a current-carrying conductor.
• I can apply Fleming's Left Hand Rule to a current-carrying wire in 3D (dots/crosses notation).
• I can state the definition of electromagnetic induction word-for-word.
• I can describe what happens as a magnet is moved in/out/held still relative to a coil, and what increases the induced e.m.f.
• I understand why induced e.m.f is minimum when flux is maximum in a rotating coil (and vice versa).
• I can explain how a transformer works, including why it needs AC (not DC) and a soft iron core.
• I can state and apply Faraday's Law: ε = Δ(NΦ)/Δt.
• I can state Lenz's Law word-for-word and explain it in terms of conservation of energy.
• I can explain the meaning of the minus sign in ε = −d(NΦ)/dt.