Electric Charge and Basic Properties

Introduction

Electrostatics is the branch of physics that deals with electric charges at rest. We encounter electric forces and phenomena in everyday life, from static cling when clothes come out of a dryer to the force that holds atoms and molecules together. The study of electrostatics begins with the fundamental concept of electric charge and the forces between charges.

Historically, phenomena related to electric charge were observed long ago. Ancient Greeks noticed that rubbing amber (elektron in Greek) could attract light objects. These early observations marked the beginning of understanding electricity.

Electric charge is a fundamental property of matter, like mass. Particles possess charge, and this charge gives rise to electric forces between them and electric fields around them. Understanding the nature of electric charge and its interactions is the first step towards comprehending a wide range of electrical and electronic phenomena.

In this topic, we will introduce the concept of electric charge, explore its basic properties, discuss how charge is distributed in different materials, and examine how objects can become charged.

Electric Charge

Electric charge is an intrinsic property of certain subatomic particles that governs their electromagnetic interactions. There are two types of electric charge: positive charge and negative charge.

Types of Charge

• Positive Charge: Protons, located in the nucleus of an atom, carry a positive charge.
• Negative Charge: Electrons, orbiting the nucleus of an atom, carry a negative charge.
• Neutral: Neutrons, also in the nucleus, have no net charge; they are electrically neutral.

The magnitude of the charge on a proton is exactly equal to the magnitude of the charge on an electron. The electron's charge is conventionally taken as negative, and the proton's charge as positive. The basic unit of charge is the magnitude of the charge of an electron or proton, denoted by $e$. $ e \approx 1.602 \times 10^{-19} $ Coulombs.

Interactions between Charges (Electrostatic Force)

Charges exert forces on each other. These forces are called electrostatic forces.

• Like charges repel each other: Two positive charges repel each other, and two negative charges repel each other.
• Unlike charges attract each other: A positive charge and a negative charge attract each other.

The strength of the electrostatic force between two point charges is described by Coulomb's Law (which will be discussed in detail later). The force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Origin of Charge in Objects

Ordinary matter is made up of atoms, which contain protons (positive charge) and electrons (negative charge). In a neutral atom, the number of protons in the nucleus is equal to the number of electrons orbiting the nucleus, so the total positive charge balances the total negative charge, resulting in a net charge of zero.

Objects become electrically charged when there is an imbalance between the number of protons and electrons.

• If an object loses electrons, it has more protons than electrons and acquires a net positive charge.
• If an object gains electrons, it has more electrons than protons and acquires a net negative charge.

Charging usually involves the transfer of electrons, as protons are tightly bound within the atomic nucleus and are not easily transferred in everyday processes like rubbing.

Units of Charge

The SI unit of electric charge is the Coulomb (C). It is named after the French physicist Charles-Augustin de Coulomb. One Coulomb is defined based on the electric current; it is the amount of charge that passes through a cross-section of a conductor in one second when the current is one Ampere. $1 \text{ C} = 1 \text{ A} \cdot \text{s}$.

The elementary charge $e$ is the magnitude of the charge of an electron or proton:

$ e \approx 1.602 \times 10^{-19} $ C.

This means one Coulomb is an extremely large amount of charge. The number of elementary charges in 1 Coulomb is $1 / (1.602 \times 10^{-19}) \approx 6.24 \times 10^{18}$ elementary charges.

Conductors And Insulators

Materials differ greatly in their ability to allow electric charge to flow through them. Based on this property, materials are classified as conductors, insulators, or semiconductors.

Conductors

Conductors are materials that allow electric charge (usually electrons) to move freely through them. In conductors, some of the electrons in the atoms (called free electrons or conduction electrons) are not tightly bound to individual atoms and can move throughout the material. When an electric field is applied across a conductor, these free electrons drift, creating an electric current.

Examples of good conductors include:

• Most metals (e.g., copper, aluminium, silver, gold, iron).
• Electrolytes (ionic solutions).
• Ionised gases (plasma).
• The Earth itself (often treated as a conductor for grounding).

Conductors are used in electrical wires, cables, and components where charge transfer is required.

Insulators (Dielectrics)

Insulators (also called dielectrics) are materials that do not allow electric charge to move freely through them. In insulators, the electrons are tightly bound to their respective atoms and are not free to roam throughout the material. Applying an electric field to an insulator causes the charges within the atoms to shift slightly (polarization), but there is no continuous flow of charge under normal conditions.

Examples of good insulators include:

• Non-metals (e.g., plastic, rubber, glass, wood, ceramics, paper, dry air).

Insulators are used to prevent the flow of electric charge, such as in the coatings of electrical wires, insulating handles of tools, or as dielectric materials in capacitors.

Semiconductors

Semiconductors are materials whose electrical conductivity is between that of conductors and insulators. Their conductivity can be significantly changed by factors like temperature, light, or the addition of impurities (doping). Semiconductors are the basis of modern electronics (transistors, diodes, integrated circuits).

Examples include silicon (Si), germanium (Ge), and gallium arsenide (GaAs).

The distinction between conductors, insulators, and semiconductors is not absolute and depends on factors like temperature and the magnitude of the electric field. Under extremely high electric fields, even insulators can break down and conduct electricity.

Charging By Induction

An object can become electrically charged without direct contact with another charged object. This process is called charging by induction.

Charging by induction involves bringing a charged object near a neutral conductor, causing a separation of charges within the conductor due to the electrostatic force. The conductor is then temporarily grounded to allow some charge to either leave or enter the conductor, resulting in a net charge opposite to that of the inducing charged object.

Steps in Charging by Induction (Example: Charging a conductor positively)

(Image Placeholder: A sequence of diagrams showing the steps of charging by induction: 1) A neutral conductor (e.g., a metal sphere on an insulating stand) with charges evenly distributed. 2) A negatively charged rod is brought near the conductor. Show positive charges accumulating on the near side of the conductor (attracted by the negative rod) and negative charges accumulating on the far side (repelled by the negative rod). The conductor is still neutral overall. 3) The far side of the conductor is connected to the ground by a wire (grounding). Show negative charges flowing from the conductor to the ground (or positive charges flowing from ground to conductor - depending on convention, electron flow is more accurate). 4) The grounding wire is removed. The positive charges remain on the conductor due to the attraction of the negatively charged rod. 5) The charged rod is removed. The positive charges redistribute themselves uniformly over the conductor. The conductor now has a net positive charge.)

To charge a neutral conductor positively:

1. Bring a negatively charged object (e.g., a rod) near the neutral conductor (e.g., a metal sphere supported by an insulating stand) without touching it.
2. The negative charge on the rod repels the free electrons in the conductor to the side farthest from the rod, leaving an excess of positive charge on the side nearest to the rod. The conductor is still electrically neutral, but the charges are separated (polarised).
3. Connect the conductor to the Earth (grounding). The Earth is a large reservoir of charge. The excess negative charge on the far side of the conductor flows from the conductor to the Earth (or, if we consider positive charge movement conceptually, positive charge flows from Earth to neutralize the negative charge on the far side).
4. Remove the connection to the Earth. The conductor is now left with an excess of positive charge on the side near the charged rod, held there by the electrostatic attraction of the negative rod.
5. Remove the charged rod. The excess positive charge redistributes itself uniformly over the surface of the conductor. The conductor is now positively charged.

To charge a neutral conductor negatively by induction, a positively charged object is used as the inducing charge. In this case, electrons are attracted from the ground to the conductor when it is grounded, resulting in a net negative charge on the conductor.

Important points about charging by induction:

• The charged object used for induction does not lose any charge; it only induces charge separation.
• The final charge on the conductor has the opposite sign to the inducing charge.
• Charging by induction requires a conductor that can allow charge movement and a connection to ground (or another conductor) to allow charge transfer.

Electroscope

An electroscope is a simple instrument used to detect the presence and type of electric charge on an object. A common type is a gold-leaf electroscope, which uses two thin gold leaves attached to a metal rod inside a case. Bringing a charged object near the cap of the rod (charging by induction) or touching the cap with a charged object (charging by conduction) causes charge to flow to the leaves, which then repel each other and diverge if charged. The extent of divergence indicates the amount of charge. Comparing the divergence when touched by a known charge helps determine the type of unknown charge.

Basic Properties Of Electric Charge

Electric charge has several fundamental properties that govern its behaviour and interactions. These properties are established through experiments and are considered cornerstones of electromagnetism.

Additivity Of Charges

The additivity of electric charges means that the total charge of a system is the algebraic sum of all the individual charges present in the system. Charge is a scalar quantity, and it can be positive or negative. When adding charges, their signs must be taken into account.

If a system contains charges $q_1, q_2, q_3, ..., q_n$, the total charge ($Q_{total}$) of the system is:

$ Q_{total} = q_1 + q_2 + q_3 + ... + q_n = \sum_{i=1}^{n} q_i $

For example, if a system contains $+5$ C of charge and $-3$ C of charge, the total charge is $(+5) + (-3) = +2$ C.

This property is important for calculating the net charge of an object or a system of particles.

Charge Is Conserved

The conservation of electric charge is a fundamental law of physics. It states that the total electric charge in an isolated system remains constant; charge can neither be created nor destroyed, only transferred from one object to another.

In any process, the net charge before the process is equal to the net charge after the process. For example, when a glass rod is rubbed with a silk cloth, electrons are transferred from the glass to the silk. The glass rod becomes positively charged (loses electrons), and the silk cloth becomes negatively charged (gains electrons). The magnitude of the positive charge on the rod is equal to the magnitude of the negative charge on the cloth. The total charge of the rod-cloth system remains zero, just as it was before rubbing.

Charge conservation applies to all known physical processes, including particle creation and annihilation. For instance, when an electron (charge $-e$) and a positron (anti-electron, charge $+e$) collide and annihilate, they produce gamma rays (photons, neutral). The total charge before ($(-e) + (+e) = 0$) is equal to the total charge after (0).

The law of conservation of charge is one of the most precise and well-tested conservation laws in physics.

Quantisation Of Charge ($ q = \pm ne $)

The quantisation of electric charge means that electric charge is not continuous; it exists in discrete packets. The smallest unit of free charge that can exist is the magnitude of the charge of an electron or proton, the elementary charge $e$.

Any observable charge $q$ is always an integer multiple of this elementary charge $e$.

$ q = \pm ne $

where $n$ is a positive integer (1, 2, 3, ...), and $e$ is the elementary charge ($e \approx 1.602 \times 10^{-19}$ C).

This means that you can have a charge of $+e, -e, +2e, -2e, +100e, -100e$, etc., but you cannot have a charge of $+0.5e$ or $+1.7e$ or any other non-integer multiple of $e$.

The quantisation of charge was experimentally demonstrated by Robert Millikan in his famous oil-drop experiment (though the concept was suggested earlier by Faraday's laws of electrolysis).

Elementary particles like quarks have fractional charges ($+2/3 e$ or $-1/3 e$), but quarks are not observed to exist freely; they are always confined within composite particles like protons and neutrons (which have integer or zero total charge). Thus, for free charges, the elementary charge $e$ is the fundamental unit.

In macroscopic systems, where charges involve billions of elementary charges, the discrete nature of charge is often not noticeable, and charge can be treated as if it were continuous. However, at the atomic and subatomic levels, quantisation is a fundamental aspect of charge.

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