Electrostatics

Electric Charge

All matter contains electric charge. There are two types: positive (carried by protons in the nucleus) and negative (carried by electrons in the outer shells). The unit of charge is the coulomb (C).

Elementary charge: e = 1.6 × 10⁻¹⁹ C (the magnitude of charge on one electron or one proton)

Like charges repel each other.
Unlike charges attract each other.
A neutral object has equal numbers of protons and electrons.

Methods of Charging

1. Friction: When two different materials are rubbed together, electrons are transferred from one to the other. The material that gains electrons becomes negatively charged; the one that loses electrons becomes positively charged. Example: plastic rod rubbed with fur — the rod gains electrons and becomes negative.

2. Conduction: A charged object is brought into direct contact with a neutral conductor. Charge spreads from the charged object to the neutral one. Both objects end up with the same sign of charge. The charge shared depends on the sizes of the objects.

3. Induction: A charged object is brought near (but does not touch) a neutral conductor. The near side of the conductor develops the opposite charge; the far side develops the same charge as the inducing object. If the conductor is earthed (connected to ground) while the charged object is near, electrons flow to/from earth, leaving a net charge. When the earth connection is removed before the charged object, the conductor retains a net charge opposite to the inducing charge.

Conservation of charge: charge cannot be created or destroyed. The total charge in a closed system remains constant.

Conductors and Insulators

Property	Conductor	Insulator
Free electrons?	Yes — electrons move freely	No — electrons are bound to atoms
Charge distribution	Spreads over surface	Stays where placed
Examples	Copper, aluminium, iron	Plastic, rubber, glass, wood

Coulomb's Law

The electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them:

F = kQ₁Q₂ / r²

Symbol	Meaning	Value / Unit
k	Coulomb's constant	9 × 10⁹ N·m²·C⁻²
Q₁, Q₂	Charges on the two objects	Coulombs (C)
r	Distance between the centres	metres (m)
F	Electrostatic force	Newtons (N)

The force acts along the line joining the two charges.
F is repulsive if both charges have the same sign; attractive if opposite signs.
F ∝ Q₁Q₂ — doubling one charge doubles the force.
F ∝ 1/r² — doubling the separation quarters the force (inverse square law).

Worked Example: Find the force between Q₁ = +3 μC and Q₂ = −2 μC separated by r = 0.05 m.
F = kQ₁Q₂/r² = (9×10⁹ × 3×10⁻⁶ × 2×10⁻⁶) / (0.05)²
F = (9×10⁹ × 6×10⁻¹²) / 0.0025 = 54×10⁻³ / 0.0025 = 21.6 N (attractive)

Electric Field

An electric field exists in the space around any charged object. It is defined as the force per unit positive test charge placed at that point:

E = F / q

For a point charge Q, the field strength at distance r is:

E = kQ / r²

Unit: N·C⁻¹ (or V·m⁻¹). E is a vector — its direction is the direction a positive test charge would move if placed at that point.

Electric Field Lines

Field lines start on positive charges and end on negative charges.
They never cross each other.
The density (closeness) of lines indicates the field strength — closer lines = stronger field.
Around an isolated positive point charge: radially outward.
Around an isolated negative point charge: radially inward.
Between two opposite charges: curved lines from + to −.
Between two parallel plates (opposite charges): uniform, parallel field lines pointing from + plate to − plate.

A positive test charge placed in a field accelerates in the direction of the field lines. A negative charge accelerates opposite to the field lines.

IEB Extension — Electric Potential & Superposition

Superposition principle: When more than two charges are present, the net force on any charge is the vector sum of the individual Coulomb forces from each other charge. Similarly, the net electric field at a point is the vector sum of fields due to each charge separately.

Electric potential (V): The electric potential at a point is the work done per unit positive charge to bring a test charge from infinity to that point:
V = kQ / r (unit: volt, V = J·C⁻¹)
Potential is a scalar — simply add the potentials due to each charge (no direction needed).

Work done by electric force: W = qV, where q is the charge moved through potential V. This is equivalent to W = qEd for a uniform field.

Uniform field between plates: E = V/d, where V is the potential difference between the plates and d is their separation. The field is uniform and perpendicular to the plates.

Show all working. Use k = 9 × 10⁹ N·m²·C⁻² and e = 1.6 × 10⁻¹⁹ C. Draw neat, labelled diagrams for field line questions.

Question 1

A plastic ruler is rubbed with a woollen cloth. Explain, using the concept of electron transfer, why the ruler becomes negatively charged. What charge does the cloth acquire? What principle ensures that charge is not "created" in this process?

Question 2

Two point charges Q₁ = +5 μC and Q₂ = +5 μC are placed 0.10 m apart. (a) Calculate the Coulomb force between them. (b) Is the force attractive or repulsive? (c) If the separation is halved to 0.05 m, by what factor does the force change?

Question 3

A point charge Q = −8 μC sits in space. (a) Calculate the electric field strength 0.03 m from the charge. (b) What is the direction of the field at that point? (c) Draw the electric field line pattern around this charge (at least 8 lines).

Question 4

Describe the process of charging a neutral metal sphere by induction using a positively charged rod. In your answer: (a) state what happens to the free electrons in the sphere when the rod is brought close; (b) explain what happens when the sphere is earthed while the rod is still near; (c) explain what charge the sphere has after the rod is removed.

Question 5

A small charge q = +2 × 10⁻⁶ C experiences a force of 0.06 N in an electric field. (a) Calculate the electric field strength at that point. (b) In which direction does the force on q act relative to the field lines? (c) What force would a charge of −4 × 10⁻⁶ C experience at the same point?

Question 6

A learner keeps two charges fixed at Q₁ = Q₂ = +6 μC and measures the Coulomb force F between them at four different separations r:

r (m)	0.02	0.04	0.06	0.08
F (N)	810	202.5	90	50.625

(a) For each column, calculate the value of F × r². What do you notice?
(b) Using your answer to (a), state in words the relationship between F and r that this data confirms.
(c) When r doubles from 0.02 m to 0.04 m, by what factor does F change? Is this consistent with Coulomb's law?
(d) Without recalculating F from Q₁, Q₂ and k, use the pattern in the table to predict F at r = 0.10 m.

Electric Charge

Methods of Charging

Conductors and Insulators

Coulomb's Law

Electric Field

Electric Field Lines

Charge Interaction Simulator