Electric Charges and Fields: Chapter 1

Chapter 1: Electric Charges and Fields

Overview

• Details concepts of electric charges, their properties, and the fields they generate.

Introduction

• Audible crackling and visible sparks occur when removing sweaters or synthetic clothing in dry weather.
• Lightning is a common example of electrical discharge.
• Electric shocks can be felt when opening a car door or touching a bus seat.
• These experiences result from the discharge of electric charges accumulating on insulating surfaces through friction.
• The electric charge is responsible for electrostatic phenomena.
• The focus will be on forces, fields, and potentials arising from static charges, which do not change or move with time.

Electric Charge

• Around 600 BC, the philosopher Thales of Miletus in Greece discovered that amber rubbed with wool or silk attracts light objects.
• The word 'electricity' comes from 'elektron', the Greek word for amber.
• Many pairs of materials when rubbed together exhibit similar attractive properties.
• Objects like straws, pith balls, or small paper pieces can be attracted when brought near rubbed materials.
• Glass rods rubbed with silk or wool repel each other, and the silk or wool pieces also repel each other, though glass attracts wool.
• Plastic rods rubbed with cat fur repel each other but attract the fur; plastic rods then attract glass rods and repel silk or wool.
• Through years of experimentation and analysis, it was discovered that electric charge exists in two forms.
• Objects can become electrified through rubbing, gaining electric charge.
• There are two kinds of charges which exhibit two properties: like charges repel, opposite charges attract.
• Polarity is the property differentiating the two types of charges.
• When a glass rod is rubbed with silk, the rod acquires one type of charge and the silk another.
• These charges nullify their effects when brought into contact after objects charged via rubbing have their effect voided by contact with one another, thus it was found, that unlike charges can negate.
• Benjamin Franklin named the charges positive and negative.
• Conventionally, the charge on a glass rod or cat fur is positive, and on a plastic rod or silk, it is negative.
• An object with a non-zero charge is described as electrified or charged, absent a formal charge and described then as uncharged.
• A gold leaf electroscope is a simple instrument for detecting the presence of charge using an apparatus with a vertical metal rod inside of a box, connected to two gold leaves at the bottom.
• When a charged object touches the rod, the charge spreads to the gold leaves, causing them to diverge.
• The extent of divergence indicates the amount of charge.
• All matter is made of atoms or molecules which are normally electrically neutral due to balanced charges.
• Chemical forces, atomic bonds in solids, adhesive forces of glue, and surface tension are all manifestations of electric forces between charged particles.
• To charge a neutral object, charge needs to be added or removed.
• Saying "an object is charged" means there is an excess or deficit of one type of charge.
• In solids, some electrons are loosely bound and can transfer between objects.
• An object can become positively charged by losing electrons or negatively charged by gaining them.
• When glass is rubbed with silk, electrons from the rod transfer to the silk, making the rod positive and the silk negative.
• The process does NOT create new charge, with the number of transferred electrons being a small fraction of the total.

Conductors and Insulators

• Conductors allow electricity to flow through them, containing electric charges (electrons) that can move freely.
• Metals, the human and animal body, and the earth are conductors.
• Insulators resist the flow of electricity examples of which include glass, porcelain, plastic, and nylon and prevent flow which are known as insulators.
• There is also a third category which some materials fall into, that can impede charge flow at a level between conductors and insulators and those are called semiconductors.
• Charge transferred to a conductor spreads throughout its surface; charge on an insulator stays put, a phenomenon related to topics covered in the next chapter.

Basic Properties of Electric Charge

Additivity of Charges

• Charges can be added algebraically because they’re scalars.
• In a system, the total charge is obtained by adding the charges like real numbers.
• If a system has n charges q1, q2, q3... qn, the total charge is q1 + q2 + q3 + ... + qn.
• Unlike mass charge can be positive or negative charges, where a body's mass is always positive.
• When adding charges in a system, appropriate signs must be used.

Conservation of Charge

• Electric charge is conserved an idea supported by observations about charged particles.
• The amount of charge gained by one object is exactly equal to the magnitude lost by the other, when two objects are rubbed together.
• Within an isolated system, charges can be redistributed, but the total charge remains constant.
• Although charge-carrying particles can be created or destroyed, the net charge of an isolated system cannot be changed.
• For example, a neutron decays into a proton and an electron, creating equal but opposite charges that sum to zero.

Quantization of Charge

• Experimentally established, all free charges are integral multiples of a basic unit of charge denoted by e.
• Charge q of an object is always given by q=ne where n is a positive or negative integer.
• This basic unit of charge is the magnitude of the charge on an electron or proton.
• By convention, the charge on an electron is negative (-e) while that on a proton is positive (+e).
• This fact is called quantization.
• Charge quantization was first proposed during interpreting experiments on electrolysis which was later demonstrated in 1912 by Millikan.
• The SI unit of charge is the coulomb (C).
• One coulomb is defined in terms of the unit of electric current which will be covered in a later chapter.
• According to the definition, one coulomb is the charge flowing through a wire in 1 second if the current is 1A (ampere).
• In this system, the basic unit of charge is e = 1.602192 x 10^-19 C, so -1C contains nearly 6 x 10^18 electrons.
• Static electricity rarely involves such large charges, hence smaller units like micro coulombs (1µC) = 10^-6 C or 1mC (milli coulombs) = 10^-3 C used.
• If electrons and protons are the only sources of charge in the universe, all observable charge on the world will be an integer multiple of e.
• When n₁ is the no of electrons and n₂ protons then the overall charge is n₂ × e + n₁ × (-e) = (n₂ – n₁) e.
• The size of the base unit is too small and thus not always recognizable on a large, macro scale.
• This situation can be compared to geometric concepts for a line that up close reveals is separated collection of very small points and has a similar situation to charge which from afar has quantized aspects that are unobservable.

Coulomb's Law

• Used to describe the force between two point charges, provided that the sizes of charged objects are much smaller than the distance separating them, then Coulomb's Law may be applied.
• Determined that the force between two point charges is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them, in which the force acting along the line joining the two charges.
• Equation takes the form of F=k(q₁q₂)/r² and for the convenience it can be written as F = 1/(4 πε₀) × (q₁q₂)/r² using the terms vacuum permittivity also known as the constant that is valued in SI units of ε₀ = 8.854 × 10~12 C² N¯¹ m¯²

Applying the Equation

• Force is a vector, so it's better to write Coulomb's law in vector notation designating components by vector.
• To find the forces by 2 on 1 that are in space, then find the vectors by calculating r21 = r2 - r1.
• It's important to note with vector notation can find if attractive since is the negative of which can be identified from charges.

Multiple Forces From Each Charge

• Each charge creates forces that can be calculated in terms of unit force direction which takes the the form of F₂₁ = ( 1/(4πε₀) × (q₁ q₂) /r^2) F₂₁
• Important to look at both force and charge while the relationship is same as newtons third.

Calculating Net Force

• Coulombs equation makes calculation for forces in vaccum with static charges is easy , complex situations when there is an intervening medium (like a fluid will be later encountered, while currently consider forces in systems like protons, or electrons.
• Can make comparisons by using Coulombs equations to compare the difference force and what that implies.

Electric Field

• To find the source forces, first establish at a point where the force will calculated on another point such that there is a clear indicator how an electric field is in that space and how much force exerted .
• The key takeaway to always use with the most recent equations provided.

The Concept of the Electric Field

• Has the electric field idea to create an electric field as long we know forces is a great way to express electric force with direction through fields we have a way to calculate.

Electric Field Due to a System of Charges

• Can calculate that system with multiple charges, but knowing the charge and forces involved is very important to a successful application and calculation.

Physical Meaning of Electric Field

• Electric field concept useful, and gives insight to amount of force exerted on a system's location at a given moment without even touching.