Charges, Charged Objects and Electrostatic Force

This topic is part of the HSC Physics course under the section Electrostatics.

HSC Physics Syllabus

• conduct investigations to describe and analyse qualitatively and quantitatively:

– processes by which objects become electrically charged (ACSPH002)

– the forces produced by other objects as a result of their interactions with charged objects (ACSPH103)
– variables that affect electrostatic forces between those objects (ACSPH103)

What is an Electric Charge?

Electric charge is a fundamental property of matter, responsible for electric forces and phenomena like static electricity. There are two types of electric charges: positive (+) and negative (−). Like charges repel each other, while opposite charges attract.

The standard unit of electric charge in the International System of Units (SI) is the Coulomb (symbol: C)

There are some examples of charges you should be familiar with in HSC Physics:

• Protons are subatomic particles present in the nucleus of atoms, and have a positive charge of +1.602 xx 10^{-19} \text{C}. This particular value is known as the elementary charge.
• Electrons are subatomic particles that are said to orbit the nucleus (Bohr atomic model), and have a negative charge of -1.602 xx 10^{-19} \text{C}.
• Neutrons are neutral subatomic particles present in the nucleus of atoms, having no charge.

This means 1 Coulomb of charge is equivalent to

$$\frac{1}{1.602 \times 10^{-19}} = 6.24 \times 10^{18} \, \text{protons or electrons}$$

Electrostatic Force

The interaction between charges and charged objects can be explained by electrostatic forces. These forces can be:

1. Attractive: Between opposite charges.
2. Repulsive: Between like charges.

The force between two point charges is described by Coulomb's Law. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Coulomb's Law is expressed by the following equation:

$$F = \frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r^2}$$

where

• \varepsilon_0 is the electric permittivity constant of free space = 8.854 xx 10^{-12} A2 s4 kg-1 m-3
• q_1 and q_2 are the magnitude of the two charges (unit: C)
• r is the distance between the two charges (unit: m)

Note that you can substitute only the magnitude of charges into Coulomb's Law to calculate the magnitude of electrostatic force. The direction of force is determined by considering whether the charges are alike or opposite.

By Coulomb's Law, several variables affect the magnitude and direction of electrostatic forces:

1. Magnitude of charge: More charge results in a stronger force.
2. Distance between charges: As the distance increases, the force decreases rapidly (inversely proportional to the square of the distance).
3. Medium between charges: The presence of different materials between charges can affect the force (e.g., air, vacuum, insulating materials).

Calculation Example

Calculate the force between two point charges q1 = 5 × 10–6 C and q2 = –3 × 10–6 C separated by a distance of 2.0 m.

Solution:

$$F = \frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r^2}$$

$$F = \frac{1}{4 \pi (8.854 \times 10^{-12})} \frac{(5 \times 10^{-6})(3 \times 10^{-6})}{(2)^2}$$

$$F = 3.4 \times 10^{-2} \, \text{N towards each other}$$

How Do Objects Get Charged?

All objects contain protons and electrons which contribute to the total charge. Objects can either be charged or uncharged (neutral). Objects are uncharged when there are equal number of protons and electrons. Objects are positively charged when they contain more protons than electrons. Vice versa, objects are negatively charged when they contain more electrons than protons. That is, it is the loss of gain of electrons that give charge.

This can occur through several processes:

Transfer of Charge Via Friction

When two different materials rub together, electrons (which carry negative charge) may transfer from one material to the other. Only electrons are transferred because they are mobile in conductors; protons are rigid, and not transferred because they are located in the nuclei of atoms.

The material that gains electrons becomes negatively charged, while the other becomes positively charged. The direction of electron transfer depends on the materials' relative tendency to gain or lose electrons. This relative tendency is described in the triboelectric series.

Triboelectric series of materials that are likely to be encountered in HSC Physics.

When a polyethylene rod (type of plastic) is rubbed with wool cloth, electrons are transferred from the wool cloth (greater tendency to lose electrons) to the polyethylene rod (greater tendency to gain electrons).

When a glass rod is rubbed with wool cloth, electrons are transferred from the glass rod (greater tendency to acquire positive charge / lose electrons) to the wool cloth (greater tendency to acquire negative charge / gain electrons).

In both examples, the rod and wool cloth were uncharged (neutral) in the beginning, and the total charge before and after rubbing remains constant (conservation of charge).

Conduction

When a charged object touches a neutral object, electrons can move from one to the other, charging the previously neutral object.

When a positively charged object is in contact with a neutral object, electrons are transferred from the neutral to the positively charged object. This causes the positively charged object to become less positive, and the neutral object to become positively charged due to a loss of electrons.

﻿When a negatively charged object is in contact with a neutral object, electrons are transferred from the negatively charged object to the neutral object. This causes the negatively charged object to become less negative, and the neutral object to become negatively charged due to a gain of electrons.

In both cases, charge transfer in conduction stops when electrostatic equilibrium is reached. This equilibrium is a state where the forces due to charge imbalances within and between objects are minimised, and no further net movement of charge occurs. The total charge in both objects also remains unchanged (conservation of charge).

Induction

A charged object can cause a redistribution of electrons in a nearby neutral object, creating areas of positive and negative charge without direct contact.

When an negatively charged object is placed near a neutral object, the excess electrons in the object causes electrons in the neutral object to move away (electrostatic repulsion). This causes the closer end of the neutral object to become positively charged (as the protons do not move), and the distal end to become negatively charged (due to electron movement).

Conversely, when a positively charged object is placed near a neutral object, the electrons are attracted towards the positively charged object. This causes the closer end to become negatively charged, and the distal end to become positively charged.

In both cases, there will be an attractive force between the two objects, and the total charge in both objects remains constant. Therefore, a charged object always attracts a net neutral object due to induction creating a local area of charge.

Principles of Charges

Quantisation of Charge

Since the number of protons and electrons in an object must always be discrete (i.e. a specific number), its net charge is always an integer multiple of the elementary charge. This concept is known as the quantisation of charge.

Conservation of Charge

Whenever charges are transferred or re-distributed, the total charge in the system always remains constant. This principle, known as the conservation of charge.

For example

• In conduction, the electrons move from the charged object to a neutral object, causing the neutral object to become charged. However, the total number of electrons in the two objects remains unchanged.
• In induction, the number of electrons and protons in an object remain unchanged after their re-distribution. This means the net charge of the object remains neutral.