Quantisation of Charge Revision Notes for Grade 10 NSC Matric Physical Sciences

Quantisation of Charge

What is elementary charge?

Elementary charge is the fundamental unit of electric charge in nature. It represents the smallest amount of charge that can exist independently. This basic unit is the amount of charge carried by a single electron (or proton).

The elementary charge is given the symbol e and has a value of:

$e = 1.6 \times 10^{-19} \text{ C}$

infoNote

Every electron carries a charge of $-1.6 \times 10^{-19}$ C, while every proton carries a charge of $+1.6 \times 10^{-19}$ C. The elementary charge represents the magnitude of this fundamental unit, regardless of sign.

Understanding charge quantisation

Charge quantisation means that electric charge cannot exist in any random amount. Instead, all charges in the universe consist of whole number multiples of the elementary charge.

The quantisation formula is:

$Q = ne$

Where:

Q = total charge (in coulombs)
n = number of elementary charges (whole number)
e = elementary charge ( $1.6 \times 10^{-19}$ C)

chatImportant

This is why you can never have 1.5 electrons or 2.7 protons - charge always comes in complete units of elementary charge!

Units of charge

Electric charge is measured in coulombs (C). Since the elementary charge is extremely small, we often work with larger units:

Microcoulombs (μC): $1 \text{ μC} = 1 \times 10^{-6} \text{ C}$
Nanocoulombs (nC): $1 \text{ nC} = 1 \times 10^{-9} \text{ C}$

infoNote

A coulomb represents an enormous number of elementary charges - approximately $6.25 \times 10^{18}$ electrons!

Worked example: Finding the number of electrons

lightbulbExample

Worked Example: Calculating Excess Electrons

Question: An object has an excess charge of $-1.92 \times 10^{-17}$ C. How many excess electrons does it have?

Solution:

Step 1: Identify what we know

Total charge $Q = -1.92 \times 10^{-17}$ C
Elementary charge $e = -1.6 \times 10^{-19}$ C (negative for electrons)
We need to find the number of electrons (n)

Step 2: Apply the quantisation formula

Since $Q = ne$ , we can rearrange to find n:

$n = \frac{Q}{e} = \frac{-1.92 \times 10^{-17}}{-1.6 \times 10^{-19}} = 120 \text{ electrons}$

Therefore, the object has 120 excess electrons.

Charge sharing in conducting spheres

When two identical conducting spheres on insulating stands touch each other, they share their total charge equally between them. This happens because charge can move freely in conductors.

The formula for charge sharing is:

$Q = \frac{Q_1 + Q_2}{2}$

Where $Q_1$ and $Q_2$ are the initial charges, and $Q$ is the final charge on each sphere.

lightbulbExample

Worked Example: Charge Sharing Between Conductors

Question: Two identical metal spheres have charges of -5 nC and -3 nC. They are brought together to touch, then separated. What is the final charge on each sphere?

Solution:

Step 1: Calculate total charge

Total charge = $Q_1 + Q_2 = (-5 \text{ nC}) + (-3 \text{ nC}) = -8 \text{ nC}$

Step 2: Apply charge sharing formula

Since the spheres are identical conductors, they share the charge equally:

$Q = \frac{-8 \text{ nC}}{2} = -4 \text{ nC} \text{ on each sphere}$

Conductors vs insulators in charge sharing

Understanding the fundamental difference between conductors and insulators is crucial for predicting charge behavior.

Conductors (like metal spheres):

Allow charge to move freely
Share charge equally when touching
Redistribute charge across their surface

Insulators (like plastic spheres):

Do not allow charge to move freely
Keep their original charges when touching
Charge remains localised where it was placed

chatImportant

Critical Difference: When two charged conductors touch, they always end up with equal charges. When two charged insulators touch, they keep their original charges unchanged.

The electroscope investigation

An electroscope is a sensitive device used to detect electric charge. It consists of:

A glass container
A metal rod with thin gold foil leaves attached
A metal plate at the top

How the electroscope works

The electroscope operates through the principle of electrostatic induction, which allows it to detect charge without direct contact.

When a charged object approaches the metal plate, it causes electrostatic induction:

The charged object attracts opposite charges to the metal plate
Like charges are repelled down to the gold foil leaves
The leaves acquire the same type of charge and repel each other
The leaves spread apart, indicating the presence of charge

infoNote

The electroscope doesn't need to touch the charged object to detect it - this demonstrates the power of electrostatic forces acting at a distance.

Grounding the electroscope

Grounding occurs when you connect the electroscope to the earth (usually by touching it). This allows excess charge to flow away, leaving the electroscope neutral. When the charged object is removed after grounding, the electroscope retains an opposite charge to the original object.

chatImportant

Key Point: Grounding is essential in electrostatic experiments to control and manipulate charge distribution. It provides a pathway for excess charge to flow away safely.

Polarisation in insulators

Unlike conductors, insulators cannot allow electrons to move freely through them. However, a charged object can still affect neutral insulators through polarisation.

Polarisation occurs when:

A charged object approaches a neutral insulator
The electrons in the insulator's atoms shift slightly towards or away from the charged object
This creates a slight separation of positive and negative charge within the material
The insulator remains neutral overall but has regions that are slightly more positive or negative
This allows the charged object to attract the neutral insulator

infoNote

Remember: The insulator is only polarised, not charged. No electrons are gained or lost from the material - the charges within atoms just redistribute slightly.

Investigation: Electrostatic force

Electrostatic forces follow a fundamental rule: like charges repel and unlike charges attract. You can demonstrate this with a simple experiment.

lightbulbExample

Practical Investigation: Demonstrating Electrostatic Forces

Method:

Rub a glass rod with silk to give it a positive charge
Hang a small charged ball from a string
Bring the glass rod near the ball
If the ball has the same charge as the rod, it will move away (repulsion)
If the ball has opposite charge, it will move towards the rod (attraction)

Why this happens:

Rubbing transfers electrons between materials
Glass rubbed with silk becomes positively charged (loses electrons)
Plastic rubbed with fur becomes negatively charged (gains electrons)

Real-world example

Water is made of polarised molecules. When you bring a charged balloon near a stream of water, the water molecules rotate so their opposite charges face the balloon. This causes the water stream to bend towards the charged balloon, demonstrating polarisation in action.

bookmarkSummary

Key Points to Remember:

Elementary charge ( $e = 1.6 \times 10^{-19}$ C) is the smallest unit of charge that exists independently
All charges are quantised - they must be whole number multiples of the elementary charge ( $Q = ne$ )
Conductors share charge equally when they touch, while insulators keep their original charges
Electroscopes detect charge through electrostatic induction, causing gold leaves to repel and spread apart
Polarisation allows charged objects to attract neutral insulators by causing slight charge separation within atoms

Quantisation of Charge (Grade 10 NSC Matric Physical Sciences): Revision Notes