Flux Density & F = BIL
Flux Density & F = BIL
- Gravitational fields are measured by the force on a mass, electric fields by the force on a charge. Magnetic fields are measured by the force on a current — and the definition is the most-recycled two-marker in the topic.
The definition (three bullets, two marks)
- is the force per unit current, per unit length, on a conductor placed perpendicular to the field. Mark schemes list three bullets — force per unit current, per unit length, perpendicular — any two for one mark, all three for two. Asked three times in three years with identical wording (9702/41/O/N/23 Q6(a)) (9702/41/O/N/24 Q7(a)) (9702/41/M/J/25 Q7(a)).
Symbols
- = force on the conductor (N)
- = magnetic flux density (T (tesla = N A⁻¹ m⁻¹))
- = current in the conductor (A)
- = length of conductor in the field (m)
- = angle between conductor and field (sin 90° = 1) (—)
- Only the component of the field across the current makes a force: current parallel to the field feels nothing. Every 2023–25 exam setup was perpendicular, so — but the perpendicular clause still earns its definition mark.
- Direction from Fleming's left-hand rule: First finger = Field, seCond finger = Current, thuMb = Motion (force), all at right angles. The force is always perpendicular to both the field and the current.
- is measured in the lab with a current balance: a magnet assembly sits on a top-pan balance with a wire crossing its field; switch on a known current and the balance reading changes by the BIL force (Newton's third law), giving . A Hall probe (final lesson) is the portable alternative.
Worked example
Smallest case: a wire in a field
A wire of length 5.0 cm carries 0.50 A at right angles to a field. The force on it is measured (via a balance) as N. Find .
- .
Answer