Electrostatics: Static Electricity Explained

Introduction

• Seeing a spark or hearing a crackle when removing synthetic clothes or sweaters in dry weather is an example of electric discharge.
• Lightning during thunderstorms and electric shocks from cars or metal bars after sliding from seats are other examples.
• These experiences are caused by the discharge of electric charges accumulated through rubbing insulating surfaces.
• Static electricity explains the topic.
• Static refers to something not moving or changing with time.
• Electrostatics studies forces, fields, and potentials from static charges.
• Electrical charge was first observed when amber rubbed with wool or silk attracted light objects around 600 BC by Thales of Miletus in Greece.
• The word "electricity" originates from "elektron", the Greek word for amber.

Electric Charge

• Rubbing certain pairs of materials results in attraction to small objects like straw and paper.
• Two glass rods rubbed with silk or wool repel each other.
• Two strands of silk or wool also repel.
• A glass rod and wool attract each other.
• Plastic rods rubbed with cat's fur repel each other but attract the fur.
• A plastic rod attracts a glass rod but repels silk or wool used to rub the glass rod.
• The glass rod repels the fur.
• These observations resulted to understand electric charge.
• There are two types of electrification, where like charges repel, and unlike charges attract, this is polarity of charge.
• Rubbing a glass rod with silk causes each to acquire a different charge.
• Electrified glass rod loses its attractive property upon contact with silk used for rubbing
• Charges disappear when charged bodies come into contact, therefore unlike charges neutralize each other's effect.
• American scientist Benjamin Franklin named the charges positive and negative.
• The charge on glass rod or cat’s fur is positive, and plastic rod or silk is negative.
• A charged object is 'electrified' or 'charged', and a neutral object is 'electrically neutral'.

Conductors

• Gold-leaf electroscopes detect charge on a body, containing a vertical metal rod in a box attached to thin gold leaves.
• Charge flows to the leaves when an object touches the metal knob, causing divergence.
• The degree of divergence indicates the amount of charge.
• Material bodies acquire charge because matter is made of atoms/molecules.
• Materials are normally electrically neutral, containing exactly balanced charges
• Forces holding molecules/atoms together like glue or surface tension, are electrical
• Electric force is pervasive, encompassing all of life, so we must study it.
• Electrifying a neutral body involves adding or removing one kind of charge, being excess or deficit charge.
• Electrons less tightly bound to atoms are transferred.
• A body losing electrons becomes positively charged.
• Gaining electrons leads to negative charge with no new charge created.
• Transferred electrons are a small fraction of the total.
• Conductors allow electricity to pass through easily, containing free moving electrons, such as metals, human/animal bodies, and Earth.
• Insulators strongly resist electricity such as glass, porcelain, plastic, nylon, and wood
• A semiconductor provides intermediate resistance between a conductor and insulator.
• Charge distributes across the entire surface of a conductor, staying in place on an insulator.
• This is why a nylon/plastic comb is electrified when combing dry hair, but a metal article is not.
• Metal charges leak to the ground through our bodies being conductors.
• A metal rod with a plastic or wooden handle shows charging when rubbed without touching the metal part.

Properties of Electric Charge

• There are positive and negative charges whose effects tend to cancel.
• Charged bodies with sizes small relative to distances are treated as point charges.
• The charge content is concentrated at one point in space.

Additivity of Charges

• If a system has two point charges q1 and q2, it's total charge is obtained algebraically
• Charges add up like real numbers/scalars like body mass.
• System with n charges (q1, q2,...qn), total charge is q1 + q2 + q3+...qn with magnitude but no direction similar to mass.
• Mass of a body is always positive, while charges can be positive or negative.
• Signs should be used in adding charges.
• The total charge of the system is (+1) + (+2) + (-3) + (+4) + (-5) = -1 in arbitrary units when +1, +2, -3, +4, and -5.

Charge is Conserved

• Charging bodies by rubbing involves transfer of electrons rather than creation/destruction of charges.
• What one body gains charging is what the other loses.
• An isolated system will have redistribution of charges, but the total charge will be conserved experimentally.

Quantisation of Charge

• All free charges are integral multiples of a basic charge unit e, so a body's charge q is always given by q = ne where n is (+) or (-) interger
• The charge of an electron/proton is the basic unit of charge with electrons as negative (-e) charge and protons being positive (+e).
• Electric charge is always an integral multiple of e
• Quantisation of charge first suggested by experimental electrolysis laws done by Faraday but was experimentally demonstrated by Millikan in 1912.
• Coulomb (C) is the SI unit of charge, defined by electric current, it states one coulomb is the charge flowing in a wire in one second if the current is one ampere
• The basic unit of charge is e = 1.602192X10^-19
• There are 6 x 10^18 electrons in a charge of -1C
• Charges of this magnitude are seldom seen in electrostatics. Common to use smaller units as micro coulombs (10^-6C) and milli coulombs (10^-3C).
• If protons and electrons are only basic charges, all observable charges will be integral multiples of e.
• If a body contains n1 electrons and n2 protons, then the total charge on the body is n2 x e + n1 x (-e) = (n2 - n1)e.
• Since n1 and n2 are integers, then the difference is also an integer.
• Therefore, the charge on a body is always in integral multiple of e and can be increased or decreased in steps of e
• The step size e is so small that charges deal with few uC
• The fact that the charge of a body may increase of decrease in units of e is not visible at this scale
• Grainy nature of the charge cannot be seen therefore it appears continuous.

Examples

• One coulomb is a very large unit for many practical purposes considering that if 10^9 electrons move out of a body every second, the time to get a total charge of 1 C on the other body is roughly 200 years
• A cubic piece of copper with a side of 1 cm contains roughly 2.5 x 10^24 electrons
• Assuming a mass of one cup of water is 250g, then the molecular mass of water is 18g, one mole(6.02 x 10^23 molecules) of water is 18g which means the number of molecules in one cup of water is (250/18) x 6.02 x 10^23
• Each molecule of water contains two hydrogen atoms and one oxygen atom, and 10 electrons and 10 protons with the total positive and negative charge has the same magnitude,(250/18) x 6.02 x 10^23 x 10 x 1.6 x 10^-19 C = 1.34 x 10^7 C

Static Forces

• Coulomb's law quantitatively describes force between two point charges.
• The force has an inverse relationship to squared distance between charges with a direct relationship to the product of magnitude of the charges