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A-LEVEL 9702 · A2 · TOPIC 18
Electric fields
The chain of the topic: a field is force per unit positive charge, F = qE; Coulomb's law gives the force between point charges, from which the radial field E and the potential V both follow. Around the hexagon are the four ideas; above is what it builds on, below is where it leads.
TOPIC 18: ELECTRIC FIELDS
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
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BUILDS ON
T4 Forces & fields idea T5 Work, energy, potential T9 Charge, current, p.d. 18.1-2
18.3
18.4
18.5
TOPIC 18
ELECTRIC
FIELDS
1 · FIELD STRENGTH & UNIFORM FIELDS
A field is force per unit positive charge.
E = F / q, a vector pointing the way a +q is pushed.
Field lines run from + to −; density shows strength.
Between parallel plates the field is uniform.
F = qE
E = V / d
uniform field strength between plates a distance d apart
+ +
− −
+
F = qE
E points from + plate
to − plate, the same
at every point.
2 · COULOMB'S LAW
Two point charges push or pull along the line joining them.
Force is proportional to each charge, inverse-square in r.
Like charges repel; unlike charges attract.
A charged sphere acts as a point charge at its centre.
F = Q₁Q₂ / (4πε₀r²)
+
+
F
F
r
Q₁
Q₂
like charges: equal and opposite forces, pushed apart
3 · FIELD OF A POINT CHARGE
A point charge has a radial, inverse-square field.
Divide Coulomb's force by the test charge: E = F / q.
Lines point outward from +Q, inward toward −Q.
Same inverse-square shape as the gravitational field.
E = Q / (4πε₀r²)
+
Q
field lines spread radially; E falls as 1/r²
4 · ELECTRIC POTENTIAL
Energy per unit charge to bring it from infinity.
V is work per unit +charge moved from infinity to r.
Field is the negative potential gradient: E = −dV/dr.
Potential energy of a pair: E_p = Qq / (4πε₀r).
V = Q / (4πε₀r)
V
r
V = Q / (4πε₀r)
V → 0 as r → ∞ for a positive charge
LEADS TO
T19 Capacitance: charge stored per unit potential T13 Gravitational fields: the same inverse-square form T20 Magnetic fields: forces on moving charge Each carries one idea forward: a field stores energy, two fields share one mathematical form, and a charge in motion feels new forces.
← Builds on IGCSE: Electric fields & charge