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Notes/Physics/Paper 4/Magnetic Fields
CAIEA Level9702§20.1–20.5

Magnetic Fields

What a magnetic field is, the force on a current-carrying wire, the force on a moving charge and its circular path, the Hall effect, velocity selection, field patterns due to currents, magnetic flux and flux linkage, and Faraday's and Lenz's laws of electromagnetic induction.

230 min read 8 sub-topics
211
question parts
2021–2025 · 36 papers
12 marks
per paper
≈ 12% of the paper
2.1/3
avg difficulty
moderate
#1
most examined
of 16 topics by marks

A compass needle swings, an electric motor turns, a particle accelerator steers protons round a ring, a metal detector pings — all four are the same physics: moving charges feeling forces from magnetic fields. This note builds that physics from its definition to the law that powers the national grid: a changing magnetic field induces an e.m.f. Along the way it collects the two force laws (F=BILsin⁡θF = BIL\sin\theta for currents, F=BQvsin⁡θF = BQv\sin\theta for charges), the circular paths of charged particles, the Hall effect that measures fields, and the graph machinery that turns a BB–tt graph into an induced e.m.f.

The bank is blunt about how much this topic matters: 438 marks across 2021–2025 make Magnetic Fields the MOST-examined A2 topic on Paper 4 — rank 1 of the 16, carried by 211 question parts in 36 paper sittings — roughly 12.2 marks on every Paper 4, with a yearly haul of 95, 105, 73, 73, 92. The mean difficulty of 2.10 is middling — the marks are not locked behind hard algebra. They are won and lost on volume and discipline: definitions the schemes reprint word-for-word on nearly every paper (magnetic field, flux density, flux, Faraday's law, Lenz's law), direction rules (Fleming's left-hand rule) applied without a slip, and sketch conventions (field-line spacing, "top-hat" e.m.f. graphs) that pay whole marks at a time. A student who drills this note's definition list can bank a third of the topic's marks before any algebra starts.

The route through is: §01 what a magnetic field is and how field lines represent it — §02 the force on a current-carrying conductor, F=BILsin⁡θF = BIL\sin\theta, and the flux density definition built from it — §03 the force on a moving charge, F=BQvsin⁡θF = BQv\sin\theta, and why the path is a circle — §04 crossed electric and magnetic fields as a velocity selector — §05 the Hall effect, derived as the syllabus demands — §06 field patterns due to currents and the forces between parallel conductors — §07 magnetic flux, flux linkage and Faraday's law, with the graph machinery — and §08 flux cutting, Lenz's law, and the eddy-current braking and damping applications.

Before you start you should be able to

  • Use electric field strength E=F/qE = F/q and the uniform-field relation E=V/dE = V/d from the A2 Electric Fields note — the velocity selector and the Hall effect are force balances between electric and magnetic forces, and both lean on E=V/dE = V/d

  • Handle circular motion: resultant force =mv2/r= mv^2/r towards the centre, and v=2πr/Tv = 2\pi r/T linking speed, radius and period — the entire engine of §03

  • Recall current as rate of flow of charge, and the microscopic relation I=nqvAI = nqvA from AS — it derives the Hall voltage in §05

  • Resolve vectors with sin⁡θ\sin\theta and cos⁡θ\cos\theta, and take moments: torque as force × perpendicular distance — §02's rotating coil is a moments question wearing a magnetic field

  • Read graphs honestly: gradients from large triangles, values read off between gridlines, and piecewise-linear graphs treated segment by segment — §07 lives on this skill

  • Recall from AS that e.m.f. is work done per unit charge by a source, and that inside a source current flows from − to + — §08 uses it to rank the induced potentials across an aircraft's wingtips

By the end of this page you can

  • Understand that a magnetic field is a field of force produced by moving charges or permanent magnets, and represent it by field lines

  • Recall and use F = BIL sin θ for the force on a current-carrying conductor, with directions from Fleming's left-hand rule; define magnetic flux density and the tesla

  • Determine the direction of the force on a charge moving in a magnetic field; recall and use F = BQv sin θ; describe the circular motion of a charged particle in a uniform field perpendicular to its velocity

  • Derive and use V_H = BI/(ntq) for the Hall voltage; understand the Hall probe as a flux-density meter; explain velocity selection with crossed electric and magnetic fields

  • Sketch the field patterns of a long straight wire, a flat circular coil and a long solenoid; explain the forces between current-carrying conductors and determine their directions

  • Define magnetic flux (Φ = BA) and flux linkage (NΦ); recall and use Faraday's law and Lenz's law, including e.m.f. = rate of change of flux linkage and e.m.f. = Blv for a rod cutting flux

01

What a magnetic field is; field lines

Syllabus requirement · §20.1

“

understand that a magnetic field is an example of a field of force produced either by moving charges or by permanent magnets; represent a magnetic field by field lines

”

A field of force, from two sources

You have already met two fields of force: gravitational fields, which act on mass, and electric fields, which act on charge. A magnetic field is the third member of the family — a region of space in which certain objects feel a force. Which objects? Not all of them: a magnetic field ignores a charged plastic rod, a stationary electron, and a current-free copper wire. It acts on exactly three kinds of thing:

  • a current-carrying conductor — a wire with a current in it (§02);
  • a moving charge — an electron beam, an ion, any charge on the move (§03);
  • a magnetic material — iron, steel, cobalt, nickel; the stuff of permanent magnets and fridge doors.

And the field has just two sources, both of them ways of getting charge to move: permanent magnets (the aligned electron motions inside the material act together) and currents — moving charges, whether in a wire, a solenoid, or a beam. Every magnetic field in physics is made by moving charge in one form or another.

Field lines: the map and its conventions

As with gravitational and electric fields (§13 and §18), we picture the field with field lines, and the same two conventions carry the physics:

  • Direction: at any point, the field line's direction is the direction of the force that the field would exert on a north magnetic pole placed there. Outside a bar magnet, lines run from the north pole to the south pole; a compass needle simply lines up with them.
  • Density: the closer together the lines, the stronger the field at that point. Lines bunched at a magnet's poles mean the field is strongest there; lines spread wide mean a weak field.

One habit worth borrowing from the earlier fields: field-line questions are marked on conventions, not artistry. Arrows on every line, even spacing where the field is uniform, and lines that never cross — a crossing would mean two force directions at one point, which is impossible.

The definition, word-perfect

This is the most frequently asked two-mark definition in the topic — the bank asked it in 2021 and again in 2023, and the scheme's marking split never changes:

a magnetic field is a region where a force acts on (M1) — a current-carrying conductor, or a moving charge, or a magnetic material / magnetic pole (A1).

The structure is the marks. The first mark is the frame — region where a force acts on — and the second is any one of the three objects. "A region where magnets attract iron" names only the material and strands the frame mark; "a region of magnetic influence" names neither. Learn the sentence as one shape with a slot at the end, and any of the three objects fills the slot.

Key idea

A magnetic field is a region where a force acts on a current-carrying conductor, a moving charge, or a magnetic material. It is produced by moving charges or permanent magnets, and drawn with field lines: direction = force on a north pole; closer lines = stronger field.

Writing the definition for both marks
  1. 1

    Open with the frame, word for word: "a region where a force acts on …".

    The M1 is the frame itself. 'A region where magnets have an effect' or 'a region around a magnet' does not say FORCE, and the scheme pays for force.

  2. 2

    Finish with any one of the three objects: a current-carrying conductor, a moving charge, or a magnetic material.

    One object is enough for the A1 — but quoting all three is safer, because a half-remembered object ('a magnet') can drift into wording the examiner rejects.

  3. 3

    Never define it by what it does to iron alone, and never as 'a field of magnetic lines'.

    Iron-only definitions miss the frame-and-object structure; 'lines' describes the map, not the field. Both score zero on real schemes.

Invented demo — who feels the force?

A strong permanent magnet sits on a bench. State, with a reason, whether each of the following experiences a force from the magnet's magnetic field:
(i) a steel pin placed 2 cm from the magnet;
(ii) a copper wire, carrying no current, placed 2 cm from the magnet;
(iii) the same copper wire now carrying a current;
(iv) an electron at rest 2 cm from the magnet;
(v) a beam of electrons moving past the magnet.

Show full working
  1. 1

    (i) Yes. Steel is a magnetic material, and magnetic materials are one of the three objects a magnetic field acts on.

    This is the material route — the fridge-magnet case. The pin is not charged and carries no current, but 'magnetic material' needs neither.

  2. 2

    (ii) No. Copper is not a magnetic material, and with no current there is no moving charge in the wire — none of the three objects is present.

    The trap: 'metal' does not mean 'magnetic material'. Only iron, steel, cobalt, nickel and a few alloys qualify; copper and aluminium do not.

  3. 3

    (iii) Yes. The current is moving charge, so the wire is now a current-carrying conductor — the first object on the list. This is the force that turns every electric motor.

    Same wire, same magnet, one switch thrown: the current creates the third condition. §02 quantifies exactly this force.

  4. 4

    (iv) No. A magnetic field acts on a moving charge. A charge at rest feels no magnetic force — however strong the field.

    'Moving charge' is the operative phrase. Stationary is the first no-force condition, and §03 builds it into the force formula as the sin θ = 0 case.

  5. 5

    (v) Yes. The electrons are charges in motion — the second object. The beam will be deflected, as §03 shows in detail.

    Same physics as (iii), just without the wire: any moving charge responds, not only charges confined to a conductor.

Answer

(i) Yes — steel is a magnetic material. (ii) No — copper is not magnetic and carries no current. (iii) Yes — a current-carrying conductor. (iv) No — the charge is stationary. (v) Yes — a moving charge.

Every 'state whether…' question in this topic is the definition list in disguise: conductor with current, moving charge, magnetic material. Check the list, answer, move on.

Common mistakes

  • Defining a magnetic field as 'a region around a magnet where iron is attracted'.

    A region where a force acts on a current-carrying conductor, a moving charge, or a magnetic material.

    The iron-only version names one object but loses the frame mark ('region where a force acts on'), and it hides the two-thirds of the topic — currents and charges — that the definition exists to cover.

  • Drawing field lines running south to north outside a bar magnet, or with no arrows at all.

    Outside the magnet, lines run north to south, each with an arrow — the direction of the force on a north pole.

    Direction arrows carry a mark of their own in every field-line sketch. A compass's north end points along the line, which fixes the direction beyond argument.

  • Saying field lines 'show the path a particle would take'.

    Lines show the DIRECTION OF THE FORCE at each point, and their spacing shows the field's strength.

    Charged particles in magnetic fields move in circles that cross field lines at right angles — nothing like the lines. The lines are a force map, not a track.

Your turn

The two-mark definition exactly as the scheme marks it, and a field-line reading drill.

  1. 19702/41 M/J 2021 Q9(a)2 marks

    State what is meant by a magnetic field.

    Stuck? Show hint

    Two-part sentence: a frame about a region and a force, then one of three objects.

    Show solution
    1. 1

      Frame first: a magnetic field is a region where a force acts on … (M1).

      The scheme's M1 is exactly this clause. It must name a force — 'a region where magnets act' does not.

    2. 2

      Then one object: … a current-carrying conductor, or a moving charge, or a magnetic material / magnetic pole (A1).

      The scheme lists all three and asks for one. Quoting all three costs nothing and guards against a misremembered object.

    Answer

    A region where a force acts on a current-carrying conductor / a moving charge / a magnetic material (or magnetic pole).

  2. 23 marks

    The diagram shows the field lines around a bar magnet, drawn closer together near the poles than in the space between the magnet and a nearby steel plate.
    (i) State what the direction of a field line at a point represents.
    (ii) State what is represented by the lines being closer together near the poles.
    (iii) A small plotting compass is placed midway between the magnet's north pole and the steel plate. State which way the compass needle points.

    Stuck? Show hint

    (i) think force on a north pole. (iii) the needle's north end lines up with the field direction.

    Show solution
    1. 1

      (i) The direction of the force the field would exert on a north magnetic pole placed at that point (B1).

      This is the convention that fixes every arrow in every field sketch. 'Direction of the field' restates the question; the pole is the physics.

    2. 2

      (ii) The field is stronger where the lines are closer together — here, strongest at the poles (B1).

      Line density is the field-strength scale of the whole map. Examiners ask this on gravitational, electric and magnetic sketches alike.

    3. 3

      (iii) The needle points along the field lines, towards the magnet's north pole — its south-seeking end towards the magnet's north end, its north end towards the plate.

      Field lines leave a north pole, so midway to the plate they point from the pole towards the plate. A compass needle aligns with the local field direction — that is all a compass ever does.

    Answer

    (i) the direction of the force on a north magnetic pole. (ii) the field is stronger there. (iii) along the field lines, away from the magnet's north pole towards the plate.

Practise magnetic-field concept and field-line questionsReal past-paper questions · Magnetic field concept and field lines

The rest of this note

Checking your access…

Can you do all of these?

  • Define a magnetic field word-perfectly: a REGION WHERE A FORCE ACTS ON a current-carrying conductor, a moving charge, or a magnetic material (M1 for the frame, A1 for any one object)

  • Define magnetic flux density with all three clauses: force per unit LENGTH, per unit CURRENT, wire PERPENDICULAR to field — any two score 1 mark, all three score 2

  • Define the tesla: newton per ampere per metre, with the wire perpendicular to the field

  • Fleming's LEFT hand: thuMb = force/Motion, First finger = Field, seCond finger = Current — and for a charge, the second finger is the velocity of a POSITIVE charge

  • State the no-force conditions: a stationary charge, or one moving parallel (or antiparallel) to B; a wire needs a current AND a non-zero angle to the field

  • Know where θ lives: between the wire (or velocity) and the magnetic field — sin θ is largest (1) when they are perpendicular

  • N turns on a coil multiply the force (F = NBIL) and the torque; a ferrous core increases B and so increases the force or torque

  • Derive the circle: BQv = mv²/r gives r = mv/(BQ); the period T = 2πm/(BQ) is independent of speed AND radius

  • Build the Hall voltage in the marked order: carriers deflect sideways → charge piles up → transverse electric field grows → steady when electric force = magnetic force

  • Know the Hall proportions: V_H ∝ B (the probe's calibration), V_H ∝ 1/t (thin slices measure better), V_H ∝ 1/n (semiconductors, small n, give measurable voltages)

  • Velocity selection: set qE = BQv, so u = E/B = V/(Bd) — independent of q and m, which is WHY it selects by speed alone

  • Sketch a wire's field: concentric circles, spacing INCREASING with distance, direction from the right-hand grip rule (the 3-mark sketch)

  • Solenoid: uniform inside, bar-magnet pattern outside; a ferrous core increases the flux density

  • Explain forces between wires in three steps: each current makes a field → each wire sits in the OTHER's field → current ⊥ field so F = BIL acts; parallel currents attract, antiparallel repel

  • Use Newton's third law: the forces on two wires are equal in magnitude even when the currents differ — and reversing BOTH currents changes nothing

  • Define magnetic flux: product of flux density and cross-sectional area PERPENDICULAR to the field; unit weber

  • Quote Faraday's law word-perfect: induced e.m.f. ∝ rate of change of magnetic flux (linkage) — magnitude form; Lenz supplies the direction

  • Quote Lenz's law word-perfect: the direction of the induced e.m.f. is such as to oppose the change producing it

  • Convert a B–t graph to an e.m.f.–t graph: E = N × A × gradient — ramps become constant non-zero e.m.f. (top hats), flats become zero, gradient sign flips flip the e.m.f. sign

  • Rod or wings cutting flux: e.m.f. = Blv, or flux cut per second; for Lenz direction questions run the chain: induced current → magnetic force → opposes the change (the motion), then FLHR for the current direction

Now do the questions
211 real Paper 4 parts from 2021–2025, sorted by difficulty, with mark schemes
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