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

Conservation of Charge

What is conservation of charge?

Conservation of charge is one of the fundamental principles in physics. This principle tells us something very important about how charge behaves in our universe.

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Definition: The principle of conservation of charge tells us that the net charge of an isolated system remains constant during any physical process, such as when two charged objects make contact and then separate.

This means that charge cannot be created or destroyed - it can only be transferred from one object to another. When we see objects becoming charged, we are actually witnessing charge moving from one place to another, not new charge being created.

In all the examples we study in electrostatics, charge is never created or destroyed. Instead, it moves from one material to another through various processes like friction, conduction, or induction.

Conductors and insulators

Materials can be classified into two main categories based on how they handle electric charge:

Conductors

Conductors are materials that let electrons move easily through them. Examples include:

Most metals (copper, aluminium, gold)
The human body
Graphite

In conductors, some electrons are not tightly bound to individual atoms. These free electrons can move throughout the material when a charge is applied.

Insulators (non-conductors)

Insulators or non-conductors are materials that do not allow charge carriers (electrons) to move through them. Examples include:

Plastic
Glass
Rubber
Wood (when dry)

In insulators, electrons are tightly bound to the atoms in the material and cannot move freely.

How charge behaves differently

The key difference between conductors and insulators affects how charge distributes:

On insulators: If excess charge is placed on an insulator, it will stay exactly where it was put. There will be a concentration of charge in that specific area of the object.
On conductors: If excess charge is placed on a conductor, the like charges will repel each other and spread out over the entire outside surface of the object.

Charge sharing between conductors

When two identical conducting spheres on insulating stands touch each other, they share the charge evenly between them. If the initial charge on the first sphere is $Q_1$ and the initial charge on the second sphere is $Q_2$ , then the final charge on each sphere after contact is:

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

This happens because the total charge is conserved, but it redistributes equally between the identical conductors.

Arrangement of charge on conductors

The electrostatic force determines how charge arranges itself on the surface of conductors. Since charges can move freely inside conductive materials, they will position themselves to minimise repulsion.

When we place charge on a spherical conductor, the repulsive forces between individual like charges cause them to spread uniformly over the surface of the sphere. However, for conductors with irregular shapes, there is a concentration of charge near sharp points or corners of the object.

Figure 16.1 illustrates this concept, showing how charge distributes differently on conductors depending on their shape - with more concentrated charge at pointed areas and more uniform distribution on smooth, curved surfaces.

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Practical application: This principle explains why buildings often have lightning rods on their roofs. The sharp point of the lightning rod creates a high concentration of charge, which helps to safely conduct lightning strikes away from the building structure. The "spreading out" of charge would not occur if we placed the charge on an insulator, since charge cannot move within insulating materials.

Quantisation of charge

All charge in the universe comes in specific, discrete amounts. This concept is called quantisation of charge.

The elementary charge (symbol: e) is the basic unit of charge, which equals the amount of charge carried by one electron (or one proton, but with opposite sign).

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Elementary charge value: $e = 1.6 \times 10^{-19}$ C

The quantisation formula

Since all charges consist of whole numbers of elementary charges, we can write:

$Q = nq_e$

Where:

$Q$ = total charge on the object
$n$ = integer number (whole number)
$q_e$ = elementary charge $(1.6 \times 10^{-19}$ C)

This formula tells us that all other charges in the universe consist of an integer multiple of the elementary charge.

Unit of charge

Charge is measured using the SI unit called the coulomb, with symbol C.

A coulomb of charge is actually a very large amount of charge for everyday electrostatics. Therefore, we often work with much smaller units:

Microcoulombs: $1 \mu C = 1 \times 10^{-6}$ C
Nanocoulombs: $1 nC = 1 \times 10^{-9}$ C

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Worked Example: Charge quantisation

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

Solution:

Identify what we know:
- Total charge: $Q = -1.92 \times 10^{-17}$ C
- Elementary charge: $e = 1.6 \times 10^{-19}$ C
- We need to find: number of electrons (n)
Apply the quantisation formula: $Q = nq_e$
Solve for n: $n = \frac{Q}{q_e}$

$n = \frac{-1.92 \times 10^{-17} \text{ C}}{1.6 \times 10^{-19} \text{ C}}$

$n = -120$
Interpret the answer: The object has 120 excess electrons (the negative sign indicates excess electrons rather than a deficit).

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Key Points to Remember:

Charge is conserved - it cannot be created or destroyed, only transferred between objects
Conductors allow charge to move freely, while insulators keep charge fixed in place
Charge spreads uniformly on smooth conductor surfaces but concentrates at sharp points
All charge is quantised - it always comes in whole multiples of the elementary charge ( $e = 1.6 \times 10^{-19}$ C)
Use the formula $Q = nq_e$ to calculate the number of elementary charges in any object

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