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A-LEVEL 9702 · A2 · TOPIC 20
Magnetic fields
The chain of the topic: a magnetic field is defined by the force it exerts, F = BIL on a current and F = BQv on a moving charge, then currents themselves make fields, and a changing flux linkage drives an induced e.m.f. Around the hexagon are the four ideas; above is what it builds on, below is where it leads.
TOPIC 20: MAGNETIC FIELDS
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
T4 Forces T9 Current I = Anvq T12 Circular motion 20.1
20.2
20.3
20.5
TOPIC 20
MAGNETIC
FIELDS
1 · THE FIELD & ITS PATTERNS
A region where a magnet or current feels a force.
Made by moving charges, currents and permanent magnets.
Field lines run N to S; closer lines mean a stronger field.
A straight wire: concentric circles (right-hand grip rule).
A solenoid: a near-uniform field, like a bar magnet.
grip rule: thumb = I, fingers curl = B
N
S
B inside the solenoid
coil field resembles a bar magnet
2 · FORCE ON A CURRENT
A current across a field feels a sideways push.
Force is greatest when I is perpendicular to B (θ = 90°).
Direction: Fleming’s left-hand rule (F, B, I).
This defines flux density B: F per unit I per unit length.
One tesla = 1 N per amp per metre; parallel wires attract.
F = B I L sin θ
B (out of page)
I
F
F is perpendicular to both I and B
3 · FORCE ON A MOVING CHARGE
A current is moving charge, so each charge is pushed.
F is perpendicular to v, so it does no work: speed is constant.
In a uniform B the path is a circle: B Q v = m v² / r.
Hall effect: charges pile up, giving a transverse voltage.
A velocity selector passes only v = E / B (crossed fields).
F = B Q v sin θ V_H = B I / (n t q)
B into page
v
F
F always points to the centre, so a circle of radius r = mv / BQ
4 · ELECTROMAGNETIC INDUCTION
A changing flux linkage drives an e.m.f.
Magnetic flux Φ = B A; flux linkage = NΦ for N turns.
Faraday: e.m.f. equals the rate of change of flux linkage.
Lenz: the induced current opposes the change (energy is conserved).
Move a magnet into a coil and the needle deflects.
E = − d(NΦ) / dt Φ = B A
N S
push in
I
induced current opposes the motion
LEADS TO
T21 Alternating currents: generators and transformers from induction T22 Quantum physics: deflecting charged particles to probe matter A changing flux makes the e.m.f. that powers the grid; the B Q v force steers the particle beams used to study the atom.
← Builds on IGCSE: Electromagnetic effects