Physics · Lesson 20

Electrostatics & capacitors

JAMBWAECNECO

What the syllabus asks

JAMB: electrostatics, Coulomb's law, electric field and potential, capacitors and their combination, energy stored in a capacitor

WAEC: electrostatics: charges, charging by friction, contact and induction, the gold-leaf electroscope, distribution of charge on conductors, action at points, lightning conductor; Coulomb's law; electric field and field lines, electric field intensity; electric potential and potential difference; capacitors, capacitance, parallel-plate capacitor, factors affecting capacitance, series and parallel…

NECO: electrostatics: charges, charging by friction, contact and induction, the gold-leaf electroscope, distribution of charge on conductors, action at points, lightning conductor; Coulomb's law; electric field and field lines, electric field intensity; electric potential and potential difference; capacitors, capacitance, parallel-plate capacitor, factors affecting capacitance, series and parallel…

What you will learn

Explain charging by friction, contact and induction in terms of electron transfer.
Describe and use the gold-leaf electroscope.
Explain charge distribution on conductors, action at points and the lightning conductor.
State and apply Coulomb's law.
Define electric field intensity and potential, draw field patterns and use E = kQ/r², E = V/d, V = kQ/r.
Define capacitance and state the factors affecting the capacitance of a parallel-plate capacitor.
Calculate effective capacitance in series and parallel, charge, p.d. and energy stored.

Key points

Charging moves electrons: gain → negative, loss → positive; like repel, unlike attract.
Induction gives opposite charge (earth, remove earth, then remove rod); contact gives the same charge.
Electroscope: increase in divergence is the only sure test of sign.
Charge sits on the outer surface of conductors and crowds at sharp points (point action, lightning conductor).
Coulomb: F = kq₁q₂/r², k ≈ 9 × 10⁹ N m²/C²; inverse square law.
E = F/q = kQ/r² (vector); between plates E = V/d.
V = kQ/r (scalar); W = qV; 1 eV = 1.6 × 10⁻¹⁹ J.
C = Q/V = ε₀εᵣA/d; increase A or εᵣ, decrease d.
Parallel: C = C₁ + C₂; series: 1/C = 1/C₁ + 1/C₂ (same Q on each).
Energy stored = ½QV = ½CV² = Q²/2C.

Start here: Electric charge and charging by friction

Comb your dry hair on a harmattan morning and the comb will pick up small bits of paper. Pull off a nylon shirt in the dark and you may see tiny sparks and hear crackling. These are effects of static electricity: electric charge at rest.

All matter is made of atoms. Each atom has a positive nucleus (protons and neutrons) surrounded by negative electrons. A normal atom has equal numbers of protons and electrons, so it is neutral. The outer electrons of some materials are loosely held and can be rubbed off.

Charging by friction: when two different insulators are rubbed together, electrons are transferred from one to the other. The body that gains electrons becomes negative; the body that loses electrons becomes positive. Charge is not created; it is moved.

Rubbed	with	Result
Glass rod	silk	glass positive (loses electrons), silk negative
Polythene or ebonite rod	fur or wool	rod negative (gains electrons), fur positive

Only electrons move in solids; protons are locked in the nuclei. The unit of charge is the coulomb (C). The charge on one electron is e = −1.6 × 10⁻¹⁹ C, so 1 C is the charge of 1/(1.6 × 10⁻¹⁹) = 6.25 × 10¹⁸ electrons.

Law of charges: like charges repel; unlike charges attract. A charged body also attracts small uncharged objects (by induction, 21.2).

Worked example 20.1

A polythene rod rubbed with wool gains 5 × 10¹² electrons. Find its charge.

Each electron carries −1.6 × 10⁻¹⁹ C.
Q = 5 × 10¹² × (−1.6 × 10⁻¹⁹) = −8 × 10⁻⁷ C = −0.8 μC.

−8 × 10⁻⁷ C

⚠️ Common mistake: saying "positive charges moved from the silk to the glass". In solids only electrons move; the glass becomes positive by losing electrons.

💡 Exam tip: the only sure test that a body is charged is repulsion; attraction could also happen between a charged and an uncharged body.

Try it yourself. How many electrons must be removed from a neutral sphere to give it a charge of +3.2 × 10⁻⁹ C?

Show solution

3.2 × 10⁻⁹ / 1.6 × 10⁻¹⁹ = 2 × 10¹⁰ electrons.

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Practice questions

1. Find the force between charges of 4 μC and −5 μC that are 0.2 m apart.

Show worked answer

9 × 10⁹ × 20 × 10⁻¹²/0.04 = 4.5 N, attractive.

2. Find the field 0.3 m from a charge of 9 nC.

Show worked answer

9 × 10⁹ × 9 × 10⁻⁹/0.09 = 900 N/C.

3. Find the potential 0.5 m from a charge of 5 nC.

Show worked answer

9 × 10⁹ × 5 × 10⁻⁹/0.5 = 90 V.

4. Plates 5 mm apart have a p.d. of 1000 V. Find E.

Show worked answer

2 × 10⁵ V/m.

5. Find the effective capacitance of 3 μF and 6 μF in series, and in parallel.

Show worked answer

2 μF; 9 μF.

Key words

Electric charge: A property of matter causing electric forces; unit coulomb (C).
Electron: A negatively charged particle, charge −1.6 × 10⁻¹⁹ C.
Conductor: A material that allows charge to flow freely, e.g. metals.
Insulator: A material that does not allow charge to flow, e.g. glass, rubber, plastic.
Induction: Charging a body by bringing a charged object near it, without contact.
Electroscope: An instrument for detecting and testing charge.
Coulomb's law: The force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation.
Electric field: A region where a charge experiences an electric force.
Electric field intensity: Force per unit positive charge, E = F/q.
Electric potential: Work done per unit charge in bringing a positive charge from infinity to a point.
Potential difference: Work done per unit charge moving between two points; unit volt.
Capacitor: A device that stores charge, made of two conductors separated by an insulator (dielectric).

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