Year 11 Physics Module 4 ⏱ ~35 min 5 MC · 3 Short Answer Lesson 1 of 17

Electric Charge & Electrostatic Force

The Boston Museum of Science Van de Graaff generator reaches 2.5 million volts, the largest air-insulated Van de Graaff in the world. At 2.5 MV, the electrostatic force between two 250 μC charges separated by 1 m is F = kQ₁Q₂/r² = 9×10⁹ × (250×10⁻⁶)²/1 = 562 N, the weight of a 57 kg person. Charge accumulates because the generator continuously separates positive and negative charges.

Today's hook: At 2.5 MV, the electrostatic force between two 250 μC charges 1 m apart equals 562 N, the weight of a 57 kg person. How does the inverse-square law set that precise value, and why does Coulomb's Law look so much like Newton's Law of Gravitation?
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Orient and predict

Before you read, predict

During a thunderstorm, charge separates inside a cloud: the base becomes negatively charged and the top positively charged.

Predict 1: If the cloud base holds −50 C of charge and the ground below is neutral, what will happen to electrons in the ground directly beneath the cloud, attracted or repelled?

Predict 2: Two small charged spheres sit 10 cm apart and repel with a certain force. If the distance doubles to 20 cm, will the force halve, quarter, or stay the same?

Warm-up, what is the elementary charge $e$?

Learning Intentions
goals

Know

  • Charge exists as positive and negative; like repels, unlike attracts
  • The three charging processes: friction, conduction, induction
  • The elementary charge $e = 1.60 \times 10^{-19}\ \text{C}$
  • Coulomb's Law and the value of $k$

Understand

  • Why charge is conserved in all charging processes
  • How conductors and insulators differ at the electron level
  • Why Coulomb's Law is an inverse-square law
  • How Coulomb's Law is analogous to Newton's Law of Gravitation

Can Do

  • Calculate the number of electrons transferred given total charge
  • Solve Coulomb's Law problems with full units
  • Predict attraction or repulsion from charge signs
  • Explain charging by induction using electron movement
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Scan these before reading

Scan these before reading
vocab
Charge ($Q$)A fundamental property of matter, measured in coulombs (C). Positive charges carried by protons; negative by electrons.
Elementary charge ($e$)$e = 1.60 \times 10^{-19}\ \text{C}$, the magnitude of charge on a single electron or proton.
Coulomb's Law$F = kq_1q_2/r^2$, the electrostatic force between two point charges, an inverse-square law.
Conservation of chargeCharge cannot be created or destroyed, only transferred between objects.
ConductorMaterial with loosely bound electrons that move freely (e.g. copper, aluminium).
InsulatorMaterial with tightly bound electrons that cannot move freely (e.g. plastic, rubber, glass).
Cross-lesson links: M4 opens with the most fundamental electrical concept, charge and Coulomb's law. Everything in M4 flows from charge: electric fields (L02) are caused by charge; potential energy (L03) is stored by charge; circuits (L05–L11) move charge; magnetic fields (L12–L14) arise from moving charge.
Misconceptions to fix
✗ Wrong: Coulomb's Law says doubling the distance halves the force.
✓ Right: Coulomb's Law is an inverse-square law ($F \propto 1/r^2$). Doubling the distance reduces the force to one-quarter of its original value.
✗ Wrong: A neutral object has no charges inside it.
✓ Right: A neutral object contains equal numbers of positive and negative charges. It has zero net charge, not an absence of charge.
✗ Wrong: Charging by induction transfers charge to the object.
✓ Right: Induction redistributes existing charge within the object. Net charge is only gained if the object is grounded while the inducing charge is nearby.
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Electric Charge

Core Content

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Electric Charge
+5 XP

The most fundamental concept in electricity

Rub a plastic ruler against a woollen jumper and hold it near small pieces of paper, the paper leaps toward the ruler without touching it. Bring two inflated balloons, both rubbed on hair, near each other, they swing apart. These everyday observations show that something invisible has been transferred between materials, and that this something can both attract and repel.

There are two types of electric charge:

  • Positive ($+$): Carried by protons in the nucleus.
  • Negative ($-$): Carried by electrons orbiting the nucleus.

The fundamental rule of electrostatics: like charges repel, unlike charges attract.

Conservation of Charge

Electric charge cannot be created or destroyed, it can only be transferred from one object to another. If one object gains $-5\ \mu\text{C}$, another must have lost $-5\ \mu\text{C}$. The total charge in an isolated system remains constant.

Real-World Anchor
A lightning bolt is not "created" charge, it is the rapid transfer of charge that has already separated within a cloud. The cloud becomes charged by friction of ice particles colliding during updrafts; when the potential difference between cloud and ground exceeds the air breakdown voltage (~3 MV/m), a conducting path forms and charge equalises in milliseconds.
Quantisation of charge

$q = ne$   where $n$ is an integer and $e = 1.60 \times 10^{-19}\ \text{C}$

Electric charge exists in two types, positive (protons) and negative (electrons); like charges repel, unlike charges attract. Charge is conserved in all processes and is quantised: $q = ne$ where $e = 1.60 \times 10^{-19}\ \text{C}$.

Pause, copy the highlighted definition into your book before moving on.

A neutral object contains no charges at all.

When an object gains electrons, it becomes negatively charged.

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Charging Processes

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Charging Processes
+5 XP

Three ways electrons transfer between objects

We just saw that charge exists in two types and is always conserved. That raises a question: how do objects become charged in the first place? This card answers it → electrons transfer by three distinct processes: friction, conduction, and induction.

Objects become charged when electrons are transferred between them. There are three distinct processes by which this can occur.

1. Charging by Friction

When two different materials are rubbed together, electrons transfer from one to the other. The material with the stronger electron affinity becomes negatively charged (gains electrons); the other becomes positively charged (loses electrons).

Example: Rubbing a plastic rod with fur, the rod becomes negatively charged; the fur positively charged. Total charge = zero (conservation).

2. Charging by Conduction

A charged object touches a neutral object. Charge flows directly until equilibrium is reached. Both objects end up with the same type of charge.

3. Charging by Induction

A charged object is brought near (without touching) a neutral conductor. Charges redistribute. If the conductor is grounded while the charged object is still near, charge flows to or from Earth. Removing the ground then the charged object leaves the conductor with a net charge opposite to the inducing object.

HSC Exam Trap
Conduction requires physical contact; induction does not. In induction, the final charge is opposite to the inducing charge; in conduction, it is the same.

Three processes transfer charge: friction (rubbing, both objects gain opposite charges), conduction (direct contact, both end up the same charge type), and induction (no contact; requires grounding; final charge is opposite to the inducing charge).

Add the highlighted principle to your notes before the check below.

A positively charged rod is brought near a neutral metal sphere which is then grounded. After removing the ground and then the rod, the sphere is…

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Conductors and Insulators

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Conductors and Insulators
+5 XP

Why some materials allow charge to move freely

We just saw that charging processes rely on electron transfer. That raises a question: why does charge spread instantly over a metal but stay put on a plastic rod? This card answers it → it comes down to how tightly electrons are bound to the material's atoms.

Whether charge moves freely through a material depends on how tightly its electrons are bound to atoms.

PropertyConductorsInsulators
Electron mobilityOuter electrons loosely bound, free to moveElectrons tightly bound, cannot move freely
ExamplesCopper, aluminium, silver, graphitePlastic, rubber, glass, wood, air
Charging behaviourCharge spreads over entire surface quicklyCharge remains localised where deposited

Conductors have loosely bound outer electrons that move freely, so charge spreads over the surface; insulators have tightly bound electrons, so charge remains localised where deposited.

Pause, write the highlighted definition into your book.

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Coulomb's Law

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Coulomb's Law
+5 XP

The quantitative law governing forces between charges

We just saw that conductors let charge spread freely while insulators keep it localised. That raises a question: how strong is the force between two separated charged objects, and does it depend on their distance? This card answers it → Coulomb's Law quantifies exactly that force.

The force between two charged objects depends on how much charge each carries and how far apart they are. This relationship was quantified by Charles-Augustin de Coulomb in 1785.

Coulomb's Law

$$F = k\frac{|q_1 q_2|}{r^2}$$

$k = 8.99 \times 10^9\ \text{N m}^2\text{ C}^{-2}$   ·   $F$ in newtons   ·   $q$ in coulombs   ·   $r$ in metres

Key Properties

  • Direction: Like charges produce a repulsive force; opposite charges produce an attractive force.
  • Inverse square: If $r$ doubles, $F$ becomes $\tfrac{1}{4}$ as strong. If $r$ triples, $F$ becomes $\tfrac{1}{9}$ as strong.
  • Point charges: For uniformly charged spheres, $r$ is the distance between centres.

Analogy to Newton's Law of Gravitation

$F_g = G\dfrac{m_1 m_2}{r^2}$   and   $F_e = k\dfrac{q_1 q_2}{r^2}$

Both are inverse-square laws. Key differences: gravity is always attractive; electrostatic force can be attractive or repulsive. $G$ is very small ($6.67 \times 10^{-11}$); $k$ is very large ($8.99 \times 10^9$).

Worked example, Lightning Strike Force

A thundercloud base carries −45 C, with an induced +12 C region at the ground surface 800 m below. Find the electrostatic force.

  1. $F = k\dfrac{|q_1 q_2|}{r^2} = (8.99 \times 10^9) \times \dfrac{|(-45)(+12)|}{(800)^2}$
  2. Numerator: $|(-45)(+12)| = 540\ \text{C}^2$
  3. Denominator: $800^2 = 640\,000\ \text{m}^2$
  4. $F = (8.99 \times 10^9) \times \dfrac{540}{640\,000} = 7.59 \times 10^6\ \text{N}$

Answer: $F \approx 7.6\ \text{MN}$, roughly the thrust of a large rocket engine.

Coulomb's Law: $F = k|q_1 q_2|/r^2$ where $k = 8.99 \times 10^9\ \text{N m}^2\text{ C}^{-2}$. It is an inverse-square law, doubling the distance quarters the force. Like charges repel; unlike charges attract.

Pause, copy the highlighted law and formula into your book before the check below.

Two charges are separated by 0.30 m with an electrostatic force of 5.0 N. If the separation is increased to 0.90 m, the new force is…

Key formulae summary

Coulomb's Law: $F = k\dfrac{|q_1 q_2|}{r^2}$ where $k = 8.99 \times 10^9\ \text{N m}^2\text{ C}^{-2}$

Quantisation: $q = ne$ where $e = 1.60 \times 10^{-19}\ \text{C}$

Inverse square: $F \propto 1/r^2$, triple the distance, $\tfrac{1}{9}$ the force

Three of these correctly describe Coulomb's Law. Pick the odd one out.

Electric charge summary showing attraction and repulsion, Coulomb's law, field lines and charging by friction
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Activity 1, Sort and Classify: Charging Scenarios

Activity 1, Sort and Classify: Charging Scenarios
ApplyBand 3

For each scenario, identify the charging process and state whether the final object has the same or opposite charge to the original charged object.

  1. A negatively charged ebonite rod is rubbed against a woollen cloth. What is the charge on each?
  2. The same rod touches a neutral pith ball. What happens to the pith ball?
  3. The rod is brought near (not touching) a neutral conductor that is then grounded, the ground removed, and the rod taken away. What is the final charge on the conductor?

A charge of $+3.2 \times 10^{-19}\ \text{C}$ represents _____ elementary positive charges.

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Activity 2, Calculate and Interpret: Coulomb's Law

Activity 2, Calculate and Interpret: Coulomb's Law
ApplyBand 4

Two identical conducting spheres, 20 cm apart: Sphere X has $+8.0 \times 10^{-9}\ \text{C}$, Sphere Y has $-2.0 \times 10^{-9}\ \text{C}$.

  1. Calculate the initial electrostatic force between them.
  2. The spheres are touched together and separated back to 20 cm. Calculate the new force and state attractive or repulsive.
  3. Explain why the magnitude of the force changes after contact.
Wrap-up, Key Definitions

Like charges repel

Charge exists in two types: positive (protons) and negative (electrons). Objects with the same type of charge repel; opposite types attract.

Conservation of charge

Charge cannot be created or destroyed. Charging only transfers charge from one object to another.

Coulomb's Law

$F = k|q_1 q_2|/r^2$, $k = 8.99 \times 10^9\ \text{N m}^2\text{ C}^{-2}$. Inverse-square: $F \propto 1/r^2$.

Three charging processes

Friction: by rubbing. Conduction: direct contact, same charge. Induction: no contact, opposite charge.

✓

Show what you have learned

Quick recall, electric charge & Coulomb's Law
+5 XP

A fresh five-question set drawn from this lesson's bank, feedback shown immediately. +5 XP per correct · +25 XP all correct

Short Answer, 10 marks
+5 XP

UnderstandBand 3(3 marks) 3. A student rubs a plastic ruler with a cloth and finds the ruler becomes negatively charged. Explain, in terms of electron transfer, how this occurs and why the cloth must become positively charged.

ApplyBand 4(3 marks) 4. Two point charges, $q_1 = +4.0 \times 10^{-8}\ \text{C}$ and $q_2 = -6.0 \times 10^{-8}\ \text{C}$, are placed 30 cm apart in air. Calculate the magnitude of the electrostatic force between them and state whether it is attractive or repulsive.

EvaluateBand 6(4 marks) 5. A lightning protection system for a building includes a tall metal rod connected to the ground by a thick copper cable. Evaluate how this system protects the building during a thunderstorm, with reference to charge distribution, electrostatic force, and the conducting properties of the materials used.

Show all answers

Multiple choice

MC answers and explanations are shown inline as you complete each question.

Activity 1, Model Answers

  1. Friction. The rod gains electrons from the wool and becomes negatively charged. The wool loses electrons and becomes positively charged. Equal and opposite charges (conservation).
  2. Conduction. Electrons transfer from the rod to the neutral pith ball. The pith ball becomes negatively charged (same as the rod).
  3. Induction. Electrons in the conductor are repelled to the far side. Grounding allows electrons to escape to Earth. Removing the ground and rod leaves the conductor positively charged, opposite to the rod's charge.

Activity 2, Model Answers

  1. $F = k|q_1 q_2|/r^2 = (8.99 \times 10^9)(8.0 \times 10^{-9})(2.0 \times 10^{-9})/(0.20)^2 = 3.6 \times 10^{-6}\ \text{N}$ (attractive, opposite charges).
  2. Total charge after contact = $+6.0 \times 10^{-9}\ \text{C}$. Each sphere gets $+3.0 \times 10^{-9}\ \text{C}$. $F = (8.99 \times 10^9)(3.0 \times 10^{-9})^2/(0.20)^2 = 2.0 \times 10^{-6}\ \text{N}$ (repulsive).
  3. The product $|q_1 q_2|$ decreased from $16 \times 10^{-18}\ \text{C}^2$ to $9 \times 10^{-18}\ \text{C}^2$, so the force decreased. The force also changed from attractive to repulsive.

Short Answer, Model Answers

Q3 (3 marks): Electrons transfer from the cloth to the ruler during rubbing. The ruler gains excess electrons and becomes negatively charged. By conservation of charge, the cloth loses the same number of electrons and becomes positively charged, total charge of the system remains zero.

Q4 (3 marks): $F = k|q_1 q_2|/r^2 = (8.99 \times 10^9)(4.0 \times 10^{-8})(6.0 \times 10^{-8})/(0.30)^2 = 2.4 \times 10^{-4}\ \text{N}$. Attractive because the charges are opposite.

Q5 (4 marks): The lightning rod is a pointed conductor connected to Earth. Electrostatic induction concentrates charge at the sharp tip, which ionises nearby air (corona discharge) and gradually neutralises cloud charge. If lightning does strike, the thick copper cable (excellent conductor, low resistance) provides a safe path to Earth, preventing current from passing through the building. The system works by both prevention (gradual discharge) and protection (safe current path).

✓

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How did your thinking change?

The Boston Museum of Science Van de Graaff generator you read about in the hero operates at 2.5 million volts, the largest air-insulated Van de Graaff in the world. Two 250 μC charges 1 m apart produce F = kQ₁Q₂/r² = 562 N. Now look back at your Think First predictions: the cloud scenario tested the same physics, like charges repel (negative cloud base repels negative electrons in the ground surface, leaving a positive surface below). When the distance doubled, did the force halve, quarter, or stay the same?

The force quarters when distance doubles, Coulomb's Law is an inverse-square law ($F \propto 1/r^2$), the same mathematical form as the 562 N calculation from the Boston Van de Graaff.

← Module overview Next: Electric Fields & Field Lines →

Module overview · Physics · Checkpoint 1 · Module quiz