1_electrostatics charges and fields

Chapter One: Electric Charges and Fields

1.1 Introduction

• Common experiences with electric discharge include:

  • Sparks when removing synthetic clothing.

  • Lightning during thunderstorms.

  • Electric shocks from touching metal objects after sliding on seats.

• These phenomena are caused by the discharge of accumulated electric charges in the body due to rubbing insulating surfaces (static electricity).

• Electrostatics: The study of forces, fields, and potentials due to static (non-moving) charges.

1.2 Electric Charge

• Historical Discovery:

  • Thales of Miletus (circa 600 BC) discovered that amber attracted light objects when rubbed with a cloth.

  • Electricity derives from the Greek word "elektron" meaning amber.

• Charge experiments:

  • Rubbing pairs of materials can lead to attraction or repulsion of light objects.

  • Examples: Glass rubbed with silk attracts light objects, while two like-charged objects repel each other.

  • Observations concluded that there are two types of charge:

    • Like charges repel.

    • Unlike charges attract.

• Charges can be transferred from one body to another by contact.

• Polarity of Charge:

  • Charge types were designated as positive and negative by Benjamin Franklin.

  • Charge on glass rod is positive, charge on plastic is negative.

1.3 Conductors and Insulators

• Conductors: Materials that allow electricity to pass easily (e.g. metals, human body).

• Insulators: Materials that resist the flow of electricity (e.g. plastic, glass).

• Conductors allow charge to spread easily, whereas insulators retain charge in one place.

• Grounding/Earthing:

  • Excess charge can flow to the ground when connected to the earth, preventing electric shock in devices.

1.4 Charging by Induction

• Induction: Process where a charged object brings about a separation of charges in another object without direct contact.

  1. A positively charged rod approaches a neutral conductor, attracting electrons.

  2. Charge separation occurs; the conductor becomes negatively charged near the rod and positively charged away from it.

  3. If the rod is removed, charges revert to the neutral state.

1.5 Basic Properties of Electric Charge

• Additivity of Charge: Total charge of a system is the algebraic sum of individual charges (e.g., for charges +3C, -2C, and +1C, total is +2C).

• Conservation of Charge: Total charge in an isolated system remains constant; charges can only be transferred, not created or destroyed.

• Quantization of Charge: Electric charge exists in integral multiples of a basic unit (e.g., e = 1.6 × 10^-19 C).

1.6 Coulomb’s Law

• Coulomb’s Law defines the force between two point charges.

• Formula:

  • F = k * (|q1 * q2| / r^2), where F is the force, q1 and q2 are charges, r is the distance, and k is Coulomb's constant (8.99 × 10^9 N m^2/C^2).

1.7 Superposition Principle

• Forces between multiple charges can be calculated using vector addition, considering the effect of each charge individually on any given charge.

1.8 Electric Field

• The electric field (E) at a point in space is defined as the force (F) per unit positive charge (q) at that point.

• E = F/q.

• Electric field due to a point charge is directed radially outward for positive charges and inward for negative charges, with a magnitude proportional to the charge and inversely proportional to the square of the distance from the charge.

• Field Lines:

  • Visual representation of electric fields indicating direction and strength.

1.9 Electric Flux

• Electric flux (Φ) through a surface is quantified by the number of electric field lines crossing that surface, related to the field and the area of the surface.

• Φ = E * A * cos(θ), where θ is the angle between the field line and the normal to the surface.

1.10 Electric Dipole

• An electric dipole consists of two equal and opposite charges separated by a distance.

• Dipole moment (p) is defined and linked to the electric field created by dipoles.

1.11 Applications of Gauss’s Law

• Gauss’s law relates the flux of an electric field through a closed surface to the charge enclosed.

• Valid for any closed surface and particularly useful for symmetrical charge distributions:

  1. For an infinitely long line charge: [ E = \frac{\lambda}{2\pi \epsilon_0 r} ]

  2. For an infinite plane sheet: [ E = \frac{\sigma}{2\epsilon_0} ]

  3. For a charged sphere: Outside – [ E = \frac{q}{4 \pi \epsilon_0 r^2} ]; Inside – E = 0.

Summary Points

• Electric charges come in two types (positive and negative) and can result in attractive or repulsive forces.

• Charges are quantized, additive, and conserved.

• Coulomb's law details the interaction between point charges, while superposition allows the analysis of systems with multiple charges.

• Electric fields and flux provide insights into forces acting on charges and their behavior in different geometries.

Chapter One: Electric Charges and Fields

1.1 Introduction

Common experiences with electric discharge include:

• Sparks when removing synthetic clothing: The rapid movement of electrons creates an electric discharge.

• Lightning during thunderstorms: A natural phenomenon caused by the build-up and discharge of static electricity in the atmosphere.

• Electric shocks from touching metal objects: Often experienced after sliding on plastic or vinyl seats, where static charge accumulates on the body.

These phenomena arise from the discharge of accumulated electric charges in the body due to friction between insulating surfaces, known as static electricity.

Electrostatics is the area of physics that deals with the study of forces, fields, and potentials resulting from static (non-moving) electric charges.

1.2 Electric Charge

Historical Discovery:

Thales of Miletus (circa 600 BC) is credited with discovering that amber attracts light objects when rubbed with cloth. The term electricity is derived from the Greek word elektron, meaning amber.

Charge Experiments:

Rubbing pairs of materials can lead to the attraction or repulsion of light objects due to the accumulation of electric charges.

• Example: Glass rubbed with silk commonly attracts light objects. In contrast, two like-charged objects (e.g., two negatively charged items) will repel each other.

• Observations from these experiments led to two fundamental conclusions:

  • Like charges repel each other.

  • Unlike charges attract each other.

• Charges can be transferred from one body to another by physical contact.

Polarity of Charge:

Benjamin Franklin identified the convention of designating charge types as positive and negative. For example, a glass rod becomes positively charged when rubbed with silk, while materials such as plastic develop a negative charge when rubbed.

1.3 Conductors and Insulators

Conductors:

Materials that facilitate the easy flow of electric current (e.g., metals like copper and aluminum, as well as the human body). They allow charges to spread quickly across their surface.

Insulators:

Materials that resist the flow of electricity (e.g., rubber, plastic, and glass). Insulators retain static charges in one place rather than allowing them to flow.

Grounding/Earthing:

A safety measure where excess electrical charge can flow to the ground when connected, effectively neutralizing the charge and preventing electric shocks from devices.

1.4 Charging by Induction

Induction:

This process describes how a charged object can induce a separation of charges within another object without direct physical contact. For instance, when a positively charged rod approaches a neutral conductor, it attracts electrons toward it, leading to charge separation: the side nearest the rod becomes negatively charged, while the other side becomes positively charged. Removing the rod allows the charges to return to a neutral state.

1.5 Basic Properties of Electric Charge

• Additivity of Charge: The total electric charge of a system is the algebraic sum of individual charges.

  • Example: For charges of +3C, -2C, and +1C, the total charge is +2C.

• Conservation of Charge: The total electric charge in an isolated system remains constant; charges can only be transferred between objects but not created or destroyed.

• Quantization of Charge: Electric charge exists in discrete amounts as integral multiples of a fundamental unit (e.g., e = 1.6 × 10^-19 Coulombs).

1.6 Coulomb’s Law

Coulomb’s Law defines the force (F) between two point charges.

• Formula:[ F = k \frac{|q_1 q_2|}{r^2} ]Where:

  • F = electrostatic force between the charges,

  • q₁ and q₂ = magnitudes of the two charges,

  • r = distance separating the centers of the two charges,

  • k = Coulomb's constant, approximately 8.99 × 10^9 N m²/C².

1.7 Superposition Principle

This principle states that the total force on any charge in a system with multiple charges can be determined by vectorially adding the individual forces exerted by all other charges. This allows for the calculation of the net force acting on any given charge in the presence of multiple influences.

1.8 Electric Field

The electric field (E) at a specific point in space can be defined as the force (F) experienced by a unit positive charge (q) placed at that point:

• Formula:[ E = \frac{F}{q} ]The electric field produced by a point charge is directed radially outward for positive charges and inward for negative charges, with the field's magnitude inversely proportional to the square of the distance from the charge.

Field Lines:

These are visual representations of electric fields that illustrate the direction and strength of the field. The density of field lines indicates the field's strength.

1.9 Electric Flux

Electric flux (Φ) through a surface is measured by the number of electric field lines crossing that surface. It is related to the electric field and the area of the surface through which the lines pass.

• Formula:[ Φ = E \cdot A \cdot \cos(θ) ]Where θ is the angle between the electric field vector and the normal (perpendicular) to the surface.

1.10 Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a distance, typically denoted as d.

• Dipole moment (p) is defined as the product of the charge (q) and the distance (d):[ p = q \cdot d ]This dipole moment is essential in understanding the electric field produced by dipoles and their behavior in external electric fields.

1.11 Applications of Gauss’s Law

Gauss’s Law states that the electric flux (Φ) through a closed surface is proportional to the charge enclosed within that surface. This law is particularly useful for calculating electric fields in symmetrical charge distributions. Specific cases include:

• For an infinitely long line charge:[ E = \frac{\lambda}{2\pi \epsilon_0 r} ]

  • Where ( \lambda ) is the linear charge density.

• For an infinite plane sheet of charge:[ E = \frac{\sigma}{2 \epsilon_0} ]

  • Where ( \sigma ) is the surface charge density.

• For a uniformly charged sphere: Outside the sphere[ E = \frac{q}{4 \pi \epsilon_0 r^2} ]

  • Inside the sphere, the electric field is zero (E = 0).

Summary Points

• Electric charges can be classified into two types: positive and negative, resulting in attractive or repulsive forces depending on the charge types involved.

• Fundamental properties of electric charges include quantization, additivity, and conservation.

• Coulomb's Law describes the interactions between point charges, while the superposition principle enables the analysis of complex systems involving multiple charges.

• The concepts of electric fields and electric flux are crucial for understanding the forces acting on charges and their behavior within different geometrical configurations.