The whole chapter, one step at a time — every idea comes alive in the live panel on the right. Scroll down; a balloon lifts your hair, charges hop across, fields draw their own lines and a potential hill rises.
1 — What charge is
Rub a balloon on your hair and the strands stand up and follow it. The balloon has gained electric charge (q) — a basic property of matter measured in coulombs (C).
- Two kinds — positive (+) and negative (−). The smallest free charge is the electron's, e = 1.6 × 10⁻¹⁹ C.
- The golden rule — like charges repel, unlike charges attract. The negative balloon attracts your positively-left hair.
Exam point: charge comes only in whole multiples of e (it is quantised): q = ± n e.
2 — Charging by friction & conservation
Rubbing does not create charge — it just transfers electrons. Silk rubbed on glass pulls electrons off the glass: the glass turns +, the silk turns an equal −.
Conservation of chargetotal charge before = total charge after
glass: 0 → +q · silk: 0 → −q · sum stays 0
So charge is never made from nothing; it is only redistributed. This is one of the great conservation laws of physics, like the conservation of energy.
Static shock: walking on carpet rubs electrons onto you — you discharge with a spark at the next doorknob.
3 — Conductors vs insulators & earthing
- Conductors — metals, the human body, salty water: have free electrons, so charge moves easily and spreads over the surface.
- Insulators — plastic, glass, rubber: electrons are bound, so charge stays put where you placed it.
Earthinga conductor joined to the ground by a wire
excess charge flows to the huge Earth → object returns to neutral (0 V)
Why it matters: fuel tankers and computer benches are earthed so dangerous static cannot build up.
4 — Coulomb's law: force vs separation
How strong is the push or pull between two charges? Coulomb's law says the force lives along the line joining them and follows an inverse-square rule.
Coulomb's lawF = k q₁q₂ / r²
k = 9 × 10⁹ N·m²·C⁻² (in air/vacuum)
The r² in the bottom is the key: take the charges twice as far apart and the force drops to a quarter; three times as far, a ninth. It fades fast.
worked — halving the distance
F = 4 N at r. What is F at r/2?
F ∝ 1/r² → (½)² in the bottom → F × 4 = 16 N
5 — Coulomb's law: force vs charge
Now hold the distance fixed and change the amount of charge. The same law says the force is directly proportional to each charge — to the product q₁q₂.
Direct proportionF ∝ q₁q₂ (at fixed r)
double q₁ → double F · double both → ×4
worked — two charges
q₁ = 2 μC, q₂ = 3 μC, r = 0.10 m?
F = 9×10⁹ × (2×10⁻⁶)(3×10⁻⁶) / (0.1)² = 5.4 N
1 microcoulomb (μC) = 10⁻⁶ C — a tiny charge, yet 5.4 N is a real, easily felt force.
6 — The electric field E = F/q
A charge changes the space around itself. Drop a tiny test charge nearby and it feels a force — the force per unit charge is the electric field E, measured in newtons per coulomb (N/C).
Electric fieldE = F / q (units: N·C⁻¹)
point charge: E = k Q / r² · field is radial (out of +, into −)
Like a torch beam, the field of a point charge points straight out and weakens with the square of the distance — same inverse-square shape as the force.
7 — Field-line patterns
We draw the invisible field as field lines: arrows showing which way a positive test charge would be pushed. Crowded lines mean a strong field.
- Single charge — lines spray out of +, dive into −, always radial.
- Dipole (+ and −) — lines curve gracefully from the + across to the −.
- Parallel plates — straight, evenly spaced lines: a uniform field, the same everywhere between the plates.
Rules: field lines never cross, and they meet a conductor's surface at right angles.
8 — Electric potential & potential difference
Moving a charge against the field stores energy, just like lifting a ball up a hill stores gravitational energy. The energy stored per coulomb is the electric potential V, measured in volts (V).
PotentialV = W / q (joules per coulomb = volts)
point charge: V = k Q / r
potential difference: V_AB = V_A − V_B
The hill is tallest right at the charge and flattens out far away. A potential difference is just the height drop between two points — what drives current in a circuit.
worked — work from a p.d.
Move q = 2 C through V = 5 V?
W = qV = 2 × 5 = 10 J
9 — Recap & real applications
- Lightning — friction in storm clouds piles up charge until a giant spark earths it to the ground.
- Van de Graaff generator — a belt carries charge to a metal dome; touch it and your hair stands on end (like charges repel).
- Photocopier & laser printer — a charged drum holds toner only where the image is, then presses it onto paper.
- Faraday cage — charge spreads to the metal skin of a car, leaving zero field inside, so you are safe from lightning.
- Two charges, + and −; like repel, unlike attract; q = ± n e (e = 1.6 × 10⁻¹⁹ C).
- Friction only moves electrons — charge is conserved, never created.
- Conductors share charge freely; insulators hold it; earthing drains it.
- Coulomb's law: F = k q₁q₂ / r² — inverse-square in r, direct in each q.
- Electric field E = F/q (N/C); for a point charge E = kQ/r², drawn as field lines.
- Potential V = W/q (volts); for a point charge V = kQ/r; p.d. drives current.