Magnetic Fields and Forces

Having finished electric fields, we now turn to magnetism — the second of the three fundamental classical field theories. A magnetic field is produced by moving charges (currents) and permanent magnets, and it exerts forces on other moving charges and current-carrying wires. In this lesson we meet the key quantity magnetic flux density B, the force on a current-carrying conductor F = BIL sin θ, and Fleming's left-hand rule.

This lesson begins OCR H556 Module 6.3 — Electromagnetism.

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What Is a Magnetic Field?

A magnetic field is a region of space in which a moving charge (or a magnet) experiences a force. Magnetic fields are produced by:

1. Permanent magnets — ferromagnetic materials with aligned atomic magnetic moments.
2. Electric currents — moving charges always generate a magnetic field around them (Oersted's discovery, 1820).
3. Changing electric fields — at a deeper level, closely connected to the previous point.

The field is drawn as field lines which:

• Run from the north pole to the south pole outside a magnet, and south to north inside.
• Never cross or end in free space — they form closed loops.
• Are closer together where the field is stronger.

graph TD
    subgraph bar[Bar magnet field]
        N[N pole] -->|field lines| S[S pole]
        N -.->|outside| S
    end

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Magnetic Flux Density

The strength of a magnetic field at a point is characterised by the magnetic flux density, symbol B. Its SI unit is the tesla (T), defined operationally by the force on a current-carrying conductor (see below).

1 T = 1 N A⁻¹ m⁻¹

That is, a magnetic field of 1 tesla produces a force of 1 newton on a 1 metre length of wire carrying 1 ampere perpendicular to the field.

Typical magnetic field strengths:

Source	B / T
Earth's surface field	~5 × 10⁻⁵
Fridge magnet	~0.005
Loudspeaker magnet	~0.1
Strong permanent magnet (NdFeB)	~1.5
MRI scanner	1.5 – 7
Superconducting lab magnet	10 – 45

The tesla is a big unit. The Earth's field is only about 50 microtesla — five orders of magnitude smaller than a hospital MRI.

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Force on a Current-Carrying Conductor

Place a straight wire of length L carrying a current I in a uniform magnetic field of flux density B. If the wire makes an angle θ with the field, the force on it is

F = BIL sin θ

Note the sin θ — this is a point where OCR differs from some other boards, which sometimes omit the angle dependence. OCR expects you to include it whenever the wire is not perpendicular to the field. Special cases:

• θ = 90° (wire perpendicular to field): F = BIL, the maximum.
• θ = 0° (wire parallel to field): F = 0.

The direction of the force is perpendicular to both the current and the field — it is given by Fleming's left-hand rule.

Fleming's Left-Hand Rule (FBI)

Use your left hand, with the first three fingers mutually at right angles:

• First finger: direction of the Field (B)
• Second finger: direction of the Current (I)
• ThuMb: direction of the Motion (Force F)

Mnemonic: "FBI" — Force, B-field, I-current. Or "the thuMb Motion, the First Finger Field, the seCond finger Current."

graph TD
    F[Thumb: Force]
    B[First finger: B field]
    I[Second finger: Current]
    B --> F
    I --> F

Use your left hand for conventional current (positive charges). If the question involves negative charges (electrons), either swap to the right hand, or remember that electron current flows the opposite way to conventional current and use the left hand as usual.

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Worked Example — Force on a Wire

A horizontal wire 80 cm long carries a current of 3.0 A perpendicular to a horizontal magnetic field of flux density 0.15 T. Calculate the force on the wire.

F = BIL sin θ
  = 0.15 × 3.0 × 0.80 × sin 90°
  = 0.15 × 3.0 × 0.80 × 1
  = 0.36 N

The force is 0.36 N, directed vertically (up or down depending on the orientation of B and I).

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Worked Example — Wire at an Angle