Electric Charges and Fields: Electrostatics

Introduction to Electric Charges and Fields

• Experiencing a spark when taking off synthetic clothes or a sweater is a common phenomenon, especially in dry weather.
• Lightning during thunderstorms exemplifies electric discharge.
• This phenomena is due to the discharge of electric charges accumulated through rubbing insulating surfaces, known as static electricity which is the focus of discussion.
• "Static" refers to anything that does not move or change with time.
• Electrostatics studies forces, fields, and potentials arising from static charges.

Electric Charge

• The discovery that amber rubbed with wool or silk attracts light objects is credited to Thales of Miletus, Greece, around 600 BC.
• The word "electricity" comes from the Greek word "elektron," meaning amber.
• Rubbing certain materials together results in them attracting light objects like straw, pith balls, and paper.
• When two glass rods rubbed with wool/silk are brought together, they repel. Likewise, two plastic rods rubbed with cat’s fur repel, but the plastic rod attracts the glass rod.
• Pith balls touched with a charged rod repel each other, indicating the presence of electric charge.
• There exist only two types of an entity called electric charge.
• Electrification occurs when bodies like glass or plastic rods, silk, fur, and pith balls acquire electric charge on rubbing.
• Like charges repel each other, and unlike charges attract.
• Charges are transferred from rods to pith balls upon contact.
• The property differentiating the two kinds of charges is called the polarity of charge.
• When a glass rod is rubbed with silk, the rod gets one kind of charge, and the silk gets the other.
• Electrified objects lose their charge upon contact, indicating that unlike charges acquired by objects neutralize each other.
• Benjamin Franklin named the charges as positive and negative.
• By convention, the charge on a glass rod or cat's fur is positive, and that on a plastic rod or silk is negative.
• An object with an electric charge is electrified or charged, while one with no charge is electrically neutral.

Unification of Electricity and Magnetism

• Electricity and magnetism were initially treated as separate subjects.
• Oersted discovered in 1820 that an electric current deflects a compass needle.
• Ampere and Faraday stated that moving electric charges produce magnetic fields, and moving magnets generate electricity.
• Maxwell and Lorentz unified these subjects, showing their interdependence in a theory called electromagnetism.
• Electromagnetism describes most phenomena around us.
• Most forces, like friction and chemical forces, have an electromagnetic origin.
• Electromagnetic force is a fundamental force of nature.
• Maxwell's four equations play the same role in electromagnetism as Newton's laws in mechanics.
• Maxwell asserted that light is electromagnetic and its speed can be determined through electric and magnetic measurements, indicating the connection to optics.
• Electricity and magnetism are the foundation of modern technological civilization, including power, telecommunications, radio, television, and practical appliances.
• Although moving charged particles exert both electric and magnetic forces, at rest, the forces are electrical.
• Both gravitational and electric forces are long-range, but electric force is stronger by several orders of magnitude.

Gold-Leaf Electroscope

• This is a simple apparatus for detecting charge on a body.
• It consists of a vertical metal rod in a box with two thin gold leaves attached to its bottom.
• When a charged object touches the metal knob, charge flows to the leaves, causing them to diverge.
• The degree of divergence indicates the amount of charge.

Paper Strip Experiment

• White paper strips can be used to understand how the electroscope works.
• The strips get charged from ironing.
• Folding the ironed strip shows that identical charges repel each other.
• Touching a curtain rod with an electrified body transfers charge to the rod and aluminum foil, causing the foil to repel; this is similar to the effect on the leaves of an electroscope.
• Divergence of the leaves depends on the amount of charge.

Conductors and Insulators

• Matter is made of atoms and/or molecules.
• Materials are normally electrically neutral but contain balanced charges.
• Electric force is all-encompassing, influencing how molecules and atoms hold together in solids.
• To electrify a neutral body, you must add or remove one kind of charge, referring to the excess or deficit of charge.
• Solids transfer loosely bound electrons.
• A body loses electrons to become positively charged or gains electrons to become negatively charged.
• A glass rod rubbed with silk transfers electrons to the silk, charging the rod positively and the silk negatively.
• Rubbing does not create new charges, but only transfers a small number of electrons.
• Specific pairs of materials are needed to notice charging on rubbing, as only the less tightly bound electrons can be transferred between bodies getting charged.

Conductors and Insulators

• Metals with a wooden or plastic handle show charging signs when rubbed without touching the metal part.
• Charge transfer occurs from a charged plastic rod to a neutral pith ball through a copper wire, but not through a nylon thread due to differences in electrical conductivity.
• Conductors allow electricity to pass through them easily because they have electric charges (electrons) that are relatively free to move inside the material. Metals, human/animal bodies, and earth are conductors.
• Non-metals like glass, porcelain, plastic, nylon, and wood resist the passage of electricity and are called insulators.
• Transferred charge readily distributes over a conductor’s surface but stays in place on an insulator.
• Nylon/plastic combs electrify on combing dry hair because the charges on metal articles leak through the body to the ground.
• Grounding or earthing allows excess charge to disappear by passing a momentary current to the ground through a conductor.
• Earthing provides safety in electrical circuits and appliances, where a thick metal plate buried deep in the earth is connected with wires.
• Homes are wired with live, neutral, and earth wires.

Charging by Induction

• Touching a pith ball with an electrified plastic rod charges it by contact leading to repulsion from plastic rods but attraction to oppositely charged glass rods. This leads to the exploration of why an electrified rod causes attraction in light objects.
• When a positively charged rod is brought near two metal spheres, the electrons in the spheres get attracted. This leaves an excess of positive charge that accumulates on one sphere.
• The process is called induction of charge and happens almost instantly.
• Keeping the charged spheres at a small distance results in them being oppositely charged. After removing the rod, the distribution of charges becomes uniform.
• The metal spheres are evenly and oppositely charged by induction, and the glass rod loses no charge.
• The rods induce opposite charges on the near surfaces of the objects, with like charges moving to the far side when electrified rods come near light objects.

How to Charge a Metal Sphere Positively Without Touching it

• Bring a negatively charged rod near the metallic sphere kept on an insulated stand.
• Free electrons in the sphere move away, resulting in a positive charge at the near end.
• Then, connect it to the ground so more electrons flow away.
• Remove the sphere from the ground, then remove the electrified rod.
• The positive charge will spread uniformly over the sphere.

Properties of Electric Charge

• Electric charges can be positive or negative, and their effects tend to cancel each other.
• The sizes of charged bodies must be very small as compared to the distance between them to be treated as point charges. All charge content of the body is assumed to be concentrated at one point in space.

Additivity of Charges

• The total charge of a system is obtained by adding the charges algebraically.
• Charge has only magnitude and not direction, like mass.
• When adding charges in a system one must use proper signs.

Charge is Conserved

• When bodies are charged by rubbing, electrons transfer from one body to the other, and no new charges are created or destroyed.
• Within an isolated system, interactions may redistribute charges, but the total charge remains always conserved.

Quantization of Charge

• All free charges are integral multiples of a basic unit of charge denoted by e.
• Charge q on a body is always given by q = ne where n is a positive or negative integer.
• This basic unit of charge is the charge of an electon or proton. The charge that electron carries is -e and that of a proton is +e .
• The fact that electric charge is always an integral multiple of e is termed as quantisation of charge.
• In the International System of Units, a unit of charge is called a couloumb denoted by the symbol C.
• One couloumb is the charge flowing through a wire in 1 second if the current is 1A (ampere). e = 1.602192 × 10-19 C
• In electrostatics, charges of large magnitude are seldom encountered and hence smaller units 1µC (micro coulomb)= 10^(-6) C or 1mC (milli couloumb)= 10^(-3) C.
• At the macroscopic level , the fact that a body’s charge can only increase or decrease in units of e is not visible, therefore the charge appears to be continuous.

Coulomb's Law

• This is a quantitative statement about the force between two point charges.
• Forces vary inversely with the square of the distance and directly proportional to the product of the magnitude of the two charges acting along the line joining the two charges in vacuum, then the magnitude of the force between them is given by.
• F = k (q_1 q_2)/r^2
• The constant k= 1/(4πε_0) has a value of about 9 × 10^9 Nm2/C^2 and ε_0 is called the permittivity of free space.
• Coulomb discoved the law without knowing the magnitude of charge; the magnitude is discovered with the law.

Coulomb's Law in Relation to Electric Charges

• A simple way is to discover Couloub's law is to put the charge on a metallic sphere q.
• If the metallic sphere is put in contact with an identical unchared sphere the charge will spread over the two spheres then the symmetry of charge on each sphere will be q/2.
• Coulomb varied the distance for q fixed paid of charges and measures the force for different separtions. He varied the charges in pairs, keeping the distance fixed for the each pair.

Vector Notation

• The position vectors of charges q1 and q2 are r1 and r2 respectively.
• F21 is the force on q2 to q1 and denoted by F12 = (1/4πε0)((q1q2)/r21)
• When charges are placed in matter the situation is complicated by the presence of matter.
• F12=F21= -q2 =0 which agrees with Newtons third law.

Electric Charges and Fields Example 1.4

• Coulomb’s law for electrostatic force between two point charges and Newton’s law for gravitational force between two stationary point masses both have inverse square dependance dependance on the distance between the charges and masses respectively.
• Compared by finding their magnitudes (I) or an electron and proton and (II) for protons.

Electric Field

• It the charge q is reversed, then what?
• If charge q is removed, then q experiences force F equal to the charge q multiplied by the electric field.
• F(r)= Q E(r)
• Equation defines the SI unit of electric field as N/C.
• Electric field is the limit of (F/q) approaches to zero.
• An alternate unit v/m will be introduced in the next chapter.
• If q is unity, the electric field due to a charge q is numerically equal to the force exerted by it.
• A positive charge, the electric field will be directed radially outwards from the charge. On the other hand, if the negative The electric field vector, at each point, points radially inward.

Electric Field pt 2

• Magnitude of the electric field E will also depend only on the distance r. is same. Is same on a sphere with the point charge at its centre; it is a spherical sphere symmetry.
• Electric is a system of charges with position vectors r1, r2,…rn, with position vector r. Like the electric file at a point in space due to a single charge, electric force field at a point without disturbing the original charges

Electric Field

• The Electric E, is a vector quality that varies from one point to another.
• One can determine what the force on a electric charge using Coulob’s law.
• For electro statistics electric Feild is convenient, electric field is the space around a system of charges tells you the Force A electrical filed and vector it has an independent dynalmic.

Electric Field and Electric Charges

• Electrical An electron falls through a distance of 1.5 cm in a uniform distance by 2.0/10^4 N C”
• Magnitude 2.0 /10 ^N The duration between them is the formula.
• In (B) the Feild is down-words: in it we know it’s going towards the positive charge.

Calculation with Electric Charges

• The electric vector at at A due to the position vector magnitude
• Magnitude and direction that is in the same phase Electric line We have electric Feild in the last sentence, it is the vector the way that they point to the right direction/strength
• The density of the lines represent the strength of a point, all the lines point outwards because all data and magnitude can now be surrounded Can always be shown

Electric Charges and Fields

• A charge in a point that is positive and negative, show that it was connected by the wire of A of the total charge is (AI) what are all the important?
• In the space field, they saw all of the number, we saw that has and unit The strength at what the P.M is this means:
• What’s the physical?

Electric Flux

• Defined With velocity through a small Flat surface ds, in a directional Normal Surface, surface is givin and cross and then you dSn
• What it is
• We now defined with the Electic Field No Physical will happen (we cannot not observe something) We will place in area, which with us of A.s With tilt the area