Theme D · Fields · SL 8h + HL extension 6h

D.2 Electric and Magnetic Fields

What are the properties of electric and magnetic fields, and how do they differ from gravitational fields?

Electric fields and gravitational fields share a family resemblance: both obey inverse square laws, both use field lines and equipotentials, both involve the concept of potential. But electric fields have one profound difference: charge comes in two signs. Like charges repel; unlike charges attract. The gravitational force is always attractive.

Millikan's oil drop experiment was a landmark: by balancing gravitational and electric forces on charged oil droplets, he showed that charge is quantised — always a multiple of 1.6 × 10⁻¹⁹ C. This single experiment established one of the deepest regularities in nature. Magnetic fields are produced by moving charges (currents), and their field patterns — around wires, coils, and solenoids — are the basis of motors, generators, and every electromagnetic device in modern technology.

Two point charges, +3 μC and −5 μC, are separated by 0.12 m. Calculate the electrostatic force between them. Sketch the electric field pattern in the region around both charges, including field lines and three equipotential surfaces.

Key equations

Coulomb's law: F = kq₁q₂/r² where k = 1/(4πε₀) = 8.99 × 10⁹ N m² C⁻²

Electric field strength: E = F/q

Uniform field (parallel plates): E = V/d

HL Electric PE: E_p = kq₁q₂/r

HL Electric potential: V_e = kQ/r; E = −ΔV_e/Δr

HL Work done moving charge: W = qΔV_e

What students must understand

Direction of forces between charges: like repel, unlike attract
Coulomb's law F = kq₁q₂/r²; comparison with Newton's law of gravitation
Conservation of electric charge
Millikan's experiment: evidence for quantisation of charge
Charge transfer by friction, induction, and contact; earthing
Electric field strength E = F/q; field lines (direction = force on positive test charge)
Uniform electric field between parallel plates: E = V/d
Magnetic field lines: around bar magnet, straight wire, circular coil, solenoid
HL Electric PE and potential; equipotential surfaces (perpendicular to field lines; no work done on them)

Linking questions

How are electric and gravitational fields similar and different? → D.1 Gravitational Fields
How do moving charges in magnetic fields probe fundamental matter? → D.3
Charge is quantised. What other quantities are quantised? → E.2 Quantum Physics (NOS)