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Chapter 01 · Part V · Electromagnetism
Revised on ____________________
Chapter 01 · Electrostatics

Charge, the field it makes, and the energy it costs

2 sheets
2 diagrams
30 results

Formulas and conditions only — no derivations, no solved numbers. The diagrams are the reader's own.

I

Charge, force and field

VECTORS — RESOLVE BEFORE YOU ADD
I.Coulomb's law  F = 14πε0 q1 q2r² k = 9×109 S I units
II.Field  E = Fq0 a property of the point, not of a charge
III.Point charge  E = k qr²
IV.Superposition  E = Σ Ei component by component
V.In a dielectric  F → FK K = relative permittivity
VI.Ring, on the axis  E = k q x(x² + R²)3/2 maximum at x = R/√2
VII.Infinite line  E = λ2πε0 r 1/r, not 1/r²
VIII.Infinite sheet  E = σ2ε0 independent of distance
The field exists whether or not a charge sits there. “The field at the centre” and “the force on a charge at the centre” are different questions with different answers.
II

Flux and Gauss's law

SYMMETRY, OR IT GIVES YOU NOTHING
I.Flux  Φ = ∮ E·dA = E A cos θ a scalar
II.Gauss's law  ∮ E·dA = qencε0
III.Charges outside  contribute field but zero net flux
IV.Conducting sphere  E = 0 inside , E = k Qr² outside
V.Uniform charged sphere  E = k Q rR³ inside ∝ r, peaking at the surface
VI.Conductor's surface  E = σε0 twice the sheet value
rER∝ r∝ 1/r²continuous at r = R
III

Potential and energy

SCALARS — ADD THEM ARITHMETICALLY
I.Potential  V = k qr zero at infinity
II.Field from potential  Ex = − dVdx the slope, not the value
III.Work  W = q (VA − VB) zero along an equipotential
IV.Pair energy  U = k q1 q2r
V.Dipole moment  p = q d from − to +
VI.Axial field  E = 2 k pr³ · equatorial k pr³
VII.Torque and energy  τ = p × E , U = − p·E
VIII.Dipole potential  V = k p cos θr² zero on the equator, where E is not
xVE = −dV/dx
IV

Capacitors

THE MIRROR IMAGE OF RESISTORS
I.Definition  C = QV
II.Parallel plate  C = ε0 Ad with a dielectric: K times more
III.In parallel  C = C1 + C2 same V
IV.In series  1C = 1C1 + 1C2 same Q
V.Energy  U = 12 C V² = Q²2C
VI.Energy density  u = 12 ε0 E²
VII.Partly filled  C = ε0 Ad − t + t/K
VIII.Force between plates  F = Q²2 ε0 A always attractive
V

Where the marks go

FOUR ERRORS, EVERY YEAR
Where marks are lost in this chapter
1Adding fields as magnitudes. Only collinear contributions add that way — otherwise resolve first.
2Reading V = 0 as E = 0. On a dipole's equator the potentials cancel while the field vectors add.
3Reading E = 0 as V = 0. Inside a conductor the field vanishes and the potential is a non-zero constant.
4Using U = ½CV² after the battery is disconnected. Ask first which quantity is fixed — V or Q.