Magnetic Fields

This guide covers Topic 20, Magnetic fields, in full — subtopics 20.1 Concept of a magnetic field, 20.2 Force on a current-carrying conductor, 20.3 Force on a moving charge, 20.4 Magnetic fields due to currents and 20.5 Electromagnetic induction — from Cambridge International AS & A Level Physics 9702, 2025–2027 series. This is A Level content and the most extensive single topic in the electricity and magnetism strand.

Before studying this

This resource assumes electric current from Electricity: Current, Potential Difference and Resistance, and circular motion from Motion in a Circle.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 — A Level, Topic 20

20.1 Concept of a magnetic field — understanding that a magnetic field is an example of a field of force produced either by moving charges or by permanent magnets; representing a magnetic field by field lines.

20.2 Force on a current-carrying conductor — recalling and using F = BIL sin θ for the force on a current-carrying conductor in a magnetic field; understanding how the force on a current-carrying conductor can be used to define magnetic flux density, and defining the tesla; explaining the forces between current-carrying conductors and predicting the direction of these forces.

20.3 Force on a moving charge — recalling and using F = BQv sin θ for the force on a charge moving in a magnetic field; understanding how the magnetic force can provide the centripetal force needed for the circular motion of charged particles in a uniform magnetic field; deriving and using the Hall voltage V_H = BI/(ntq), and explaining how the Hall effect is used in a Hall probe to measure magnetic flux density; describing the use of crossed (perpendicular) electric and magnetic fields in velocity selection.

20.4 Magnetic fields due to currents — sketching magnetic field patterns due to currents in a long straight wire, a flat circular coil and a long solenoid; understanding that the magnetic field due to a current increases with current and decreases with distance from a current-carrying conductor; understanding the effect of a ferrous core on the strength of the magnetic field produced by a solenoid.

20.5 Electromagnetic induction — defining magnetic flux and magnetic flux linkage; recalling and using Faraday’s law of electromagnetic induction; recalling and using Lenz’s law to determine the direction of an induced e.m.f.

The magnetic field concept

A magnetic field is a field of force produced by moving charges (electric currents) or permanent magnets, represented using field lines that form closed loops, running from north to south poles outside a magnet.

Force on a current-carrying conductor

A current-carrying conductor placed in a magnetic field experiences a force:

F = BIL sin θ

where B is the magnetic flux density, I is the current, L is the length of conductor in the field, and θ is the angle between the current direction and the field. This defines magnetic flux density: the tesla is the flux density that produces a force of 1 N per metre of conductor carrying 1 A, perpendicular to the field.

Forces between current-carrying conductors

Each current-carrying conductor produces its own magnetic field, so two parallel conductors each experience a force due to the other’s field. Two wires carrying current in the same direction attract; two wires carrying current in opposite directions repel. The size of each force follows from F = BIL, with B taken as the flux density produced by one wire at the location of the other — so the force per unit length increases with both currents and decreases with the separation between the wires.

Force on a moving charge

A charge moving through a magnetic field also experiences a force:

F = BQv sin θ

Because this force acts perpendicular to velocity, it does no work and changes only the direction of motion, not its speed. When a charged particle enters a uniform field perpendicular to its velocity, this magnetic force provides exactly the centripetal force needed for uniform circular motion — connecting directly to F = mv²/r from circular motion.

Worked example. An electron (charge 1.6 × 10⁻¹⁹ C) moves at 2.0 × 10⁶ m s⁻¹ perpendicular to a magnetic field of flux density 0.50 T. The force on it:

F = BQv = 0.50 × 1.6 × 10⁻¹⁹ × 2.0 × 10⁶ = 1.6 × 10⁻¹³ N

The Hall effect and the Hall probe

When a current-carrying slice of material (typically a semiconductor) is placed in a magnetic field perpendicular to the current, the magnetic force on the moving charge carriers pushes them sideways, building up a charge imbalance across the slice until the resulting electric field exerts an equal and opposite force on the carriers. This sideways potential difference is the Hall voltage:

V_H = BI / (ntq)

where B is the magnetic flux density, I is the current, n is the number density of charge carriers, t is the thickness of the slice in the direction of B, and q is the charge on each carrier. Because V_H is proportional to B for a given slice, current and carrier density, this effect is used in a Hall probe: a calibrated Hall slice whose voltage output gives a direct reading of magnetic flux density.

Velocity selection

A velocity selector uses crossed (perpendicular) electric and magnetic fields to allow only charged particles of one particular speed through undeflected. The electric force (qE) and the magnetic force (qBv) act in opposite directions on the particle; only when these balance,

qE = qBv₀   ⟹   v₀ = E/B

does the particle pass through in a straight line — particles with any other speed experience a net sideways force and are deflected out of the beam.

Magnetic fields due to currents

A long straight current-carrying wire produces a field of concentric circles around it, whose flux density increases with current and decreases with distance from the wire. A flat circular coil produces a field resembling that of a short bar magnet at its centre. A long solenoid produces a strong, uniform field inside it, similar to a bar magnet’s field but concentrated and controllable via the current.

Placing a ferrous (iron) core inside a solenoid greatly increases the flux density produced for the same current, because the core itself becomes magnetised and adds its own much stronger field to the solenoid’s — this is the basis of an electromagnet, and is why relays and electric bells use an iron-cored coil rather than an air-cored one.

Electromagnetic induction

Magnetic flux Φ through an area is the product of magnetic flux density and the area perpendicular to the field. Magnetic flux linkage is the product of flux and the number of turns of a coil, NΦ.

Faraday’s law states that the magnitude of an induced e.m.f. is proportional to the rate of change of magnetic flux linkage. Lenz’s law states that an induced e.m.f. always acts in a direction to oppose the change producing it — this determines the direction (sign) of the induced e.m.f. and is a direct consequence of conservation of energy.

Common mistakes

• Forgetting the sin θ term in F = BIL sin θ or F = BQv sin θ — the force is maximum when the current/velocity is perpendicular to the field (θ = 90°) and zero when parallel to it (θ = 0°).
• Assuming the magnetic force on a moving charge does work on it — since the force is always perpendicular to velocity, it changes direction only, never speed or kinetic energy.
• Confusing magnetic flux (Φ, through one turn) with flux linkage (NΦ, for a coil of N turns) — Faraday’s law is stated in terms of flux linkage.
• Getting the direction from Lenz’s law wrong — the induced effect always opposes the change that caused it, never reinforces it.
• Mixing up the directions in the parallel-conductor force rule — same directions attract, opposite directions repel; check with F = BIL and the right-hand/left-hand rule rather than trying to memorise it directly.
• Forgetting that a velocity selector only passes one speed — any charge moving faster or slower than v₀ = E/B feels a net force and is deflected.

Quick revision checklist

• F = BIL sin θ, and defining the tesla from it
• Forces between current-carrying conductors: same direction attracts, opposite repels
• F = BQv sin θ, and how it provides centripetal force for charged particles in circular motion
• V_H = BI/(ntq), the Hall voltage, and how a Hall probe measures B
• Velocity selection: v₀ = E/B when the electric and magnetic forces balance
• Field patterns for a straight wire, flat coil and solenoid, and the effect of a ferrous core
• Faraday’s law (rate of change of flux linkage) and Lenz’s law (opposing direction)

Related resources

• Capacitance — the previous A Level topic
• Alternating Currents — the next A Level topic, built on electromagnetic induction
• Cambridge AS & A Level Physics hub

Written against Cambridge International AS & A Level Physics 9702, 2025–2027 series. Always check the current syllabus for your examination year.